DP Mathematics HL Questionbank

6.1
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[N/A]Directly related questions
- 18M.2.hl.TZ2.11c: Find the coordinates of the three points on C, nearest the origin, where the tangent is parallel...
- 18M.2.hl.TZ2.11b.ii: Given that the gradients of the tangents to C at P and Q are m1 and m2 respectively, show that m1...
- 18M.2.hl.TZ2.11b.i: Find the coordinates of P and Q.
- 18M.2.hl.TZ1.9c: The normal at P cuts the curve again at the point Q. Find the x-coordinate of Q.
- 18M.2.hl.TZ1.9b: Find the equation of the normal to the curve at the point P.
- 16M.2.hl.TZ2.7b: Find the value of k.
- 16M.1.hl.TZ2.4: The function f is defined as f(x)=ax2+bx+c where...
- 16M.1.hl.TZ2.11c: (i) Find d2hdt2. (ii) Find the values of...
- 16M.2.hl.TZ1.12d: Find the coordinates of the second point at which the normal found in part (c) intersects C.
- 16M.2.hl.TZ1.12c: Find the equation of the normal to C at the point A.
- 16M.2.hl.TZ1.12a: Find the value of a.
- 16M.1.hl.TZ1.10: Find the x-coordinates of all the points on the curve...
- 16N.1.hl.TZ0.11h: Find the value κ for x=π2 and comment on its meaning with respect to...
- 16N.1.hl.TZ0.11g: Find the value of the curvature of the graph of f at the local maximum point.
- 16N.1.hl.TZ0.9b: Find the equations of the tangents to this curve at the points where the curve intersects the...
- 16N.1.hl.TZ0.11b: Show that d2ydx2=2excosx.
- 17N.2.hl.TZ0.10a.i: Show that the x-coordinate of the minimum point on the curve y=f(x) satisfies the...
- 17N.1.hl.TZ0.11d: Show that, for n>1, the equation of the tangent to the curve y=fn(x) at...
- 17N.1.hl.TZ0.11c: Hence or otherwise, find an expression for the derivative of fn(x) with respect to x.
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point (1, √3).
- 17M.2.hl.TZ1.2b: Determine the equation of the tangent to C at the point...
- 17M.1.hl.TZ2.9c: By finding g′(x) explain why g is an increasing function.
- 15N.2.hl.TZ0.13a: Find f″(x).
- 15N.1.hl.TZ0.8b: Consider f(x) = \sin (ax) where a is a constant. Prove by mathematical induction that...
- 15N.1.hl.TZ0.7b: Find the coordinates of the points where the tangent to the curve is vertical.
- 15N.1.hl.TZ0.7a: Show that there is no point where the tangent to the curve is horizontal.
- 15N.1.hl.TZ0.4b: Determine the equation of the normal to the curve at the point x = 3 in the form...
- 15N.3ca.hl.TZ0.5a: Show that the tangent to the curve y = f(x) at the point (1,{\text{ }}0) is normal to the...
- 15N.3ca.hl.TZ0.2a: Show that f''(x) = 2\left( {f'(x) - f(x)} \right).
- 12M.1.hl.TZ1.9: The curve C has equation 2{x^2} + {y^2} = 18. Determine the coordinates of the four points on...
- 12M.1.hl.TZ1.12a: Show that f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}} and deduce that f...
- 12M.2.hl.TZ1.1: Given that the graph of y = {x^3} - 6{x^2} + kx - 4 has exactly one point at which...
- 12M.2.hl.TZ1.11d: Find the coordinates of the point of intersection of the normals to the graph at the points P and Q.
- 12M.1.hl.TZ2.13a: Using the definition of a derivative as...
- 12M.2.hl.TZ2.6c: Find the equation of the normal to the curve at x = 1 .
- 12M.2.hl.TZ2.6b: Write down the gradient of the curve at x = 1 .
- 08M.2.hl.TZ1.13: A family of cubic functions is defined as...
- 08M.1.hl.TZ2.8: A normal to the graph of y = \arctan (x - 1) , for x > 0, has equation...
- 08N.1.hl.TZ0.6: Find the equation of the normal to the curve 5x{y^2} - 2{x^2} = 18 at the point (1, 2) .
- 11M.1.hl.TZ2.11b: The tangent to C at the point P(1, 2) cuts the x-axis at the point T. Determine the coordinates...
- 11M.1.hl.TZ2.11c: The normal to C at the point P cuts the y-axis at the point N. Find the area of triangle PTN.
- 09M.1.hl.TZ1.7: Consider the functions f and g defined by f(x) = {2^{\frac{1}{x}}} and...
- 09N.1.hl.TZ0.12: A tangent to the graph of y = \ln x passes through the origin. (a) Sketch the graphs of...
- SPNone.1.hl.TZ0.5b: Show that f''(0) = 0 .
- SPNone.1.hl.TZ0.13a: Given that f and its derivative, f' , are continuous for all values in the domain of f , find...
- SPNone.2.hl.TZ0.13d: Find the equation of the normal to the graph of f where x = 0.75 , giving your answer in the form...
- 13M.1.hl.TZ1.7: A curve is defined by the equation 8y\ln x - 2{x^2} + 4{y^2} = 7. Find the equation of the...
- 10M.1.hl.TZ2.8: The normal to the curve x{{\text{e}}^{ - y}} + {{\text{e}}^y} = 1 + x, at the point (c,...
- 10N.2.hl.TZ0.4: Find the equation of the normal to the curve {x^3}{y^3} - xy = 0 at the point (1, 1).
- 10N.2.hl.TZ0.10: The line y = m(x - m) is a tangent to the curve (1 - x)y = 1. Determine m and the...
- 10N.1.hl.TZ0.12b: Consider the...
- 10N.1.hl.TZ0.13: Consider the curve y = x{{\text{e}}^x} and the line \(y = kx,{\text{ }}k \in...
- 13M.1.hl.TZ2.5b: Find the equation of the tangent to C at the point \left( {\frac{\pi }{2},0} \right).
- 11N.1.hl.TZ0.13a: Find the equation of the tangent to C at the point (2, e).
- 11N.1.hl.TZ0.6: Given that y = \frac{1}{{1 - x}}, use mathematical induction to prove that...
- 09M.2.hl.TZ1.12: (a) If A, B and C have x-coordinates a\frac{\pi }{2}, b\frac{\pi }{6} and...
- 14M.3ca.hl.TZ0.2a: Consider the functions f(x) = {(\ln x)^2},{\text{ }}x > 1 and...
- 14M.1.hl.TZ1.11d: The graph of y = {\text{ }}f(x) crosses the x-axis at the point A. Find the equation of...
- 14M.2.hl.TZ1.10d: Find the equation of the line {L_2}.
- 14M.1.hl.TZ2.8a: Determine whether or not fis continuous.
- 14M.2.hl.TZ2.10b: Find the equation of the normal to the curve at the point (1, 1).
- 13N.2.hl.TZ0.13a: (i) Explain why the inverse function {f^{ - 1}} does not exist. (ii) Show that the...
- 14M.2.hl.TZ1.10b: (i) Find f'(x). (ii) Show that the curve has exactly one point where its tangent is...
- 14M.2.hl.TZ1.10c: Find the equation of {L_1}, the normal to the curve at the point where it crosses the y-axis.
- 17N.2.hl.TZ0.11a.iii: Find the x-coordinate(s) of the point(s) of inflexion of the graph of y = f(x), labelling...
- 17N.2.hl.TZ0.11a.ii: Sketch a graph of y = f’(x) for 0 \leqslant x < \frac{\pi }{2}.
- 17N.2.hl.TZ0.11a.i: Determine an expression for f’(x) in terms of x.
- 17N.2.hl.TZ0.10c: Find the coordinates of the point on the graph of f where the normal to the graph is parallel...
- 17N.2.hl.TZ0.10a.ii: Determine the values of x for which f(x) is a decreasing function.
- 15M.1.hl.TZ2.4a: Determine the values of x for which f(x) is a decreasing function.
- 15M.2.hl.TZ1.9: Find the equation of the normal to the curve...
- 15M.2.hl.TZ2.12c: For t > 5, the displacement of the particle is given by...
- 15M.2.hl.TZ2.11b: Find the equation of the normal to the curve at the point (6,{\text{ }}1).
- 14N.1.hl.TZ0.11c: The graph of y = g(x) intersects the x-axis at the point Q. Show that the equation...
- 14N.1.hl.TZ0.11e: A region R is bounded by the graphs of y = g(x), the tangent T and the line...
Sub sections and their related questions
Informal ideas of limit, continuity and convergence.
- 14M.1.hl.TZ2.8a: Determine whether or not fis continuous.
- 15M.2.hl.TZ2.12c: For t > 5, the displacement of the particle is given by...
- 16M.2.hl.TZ1.12a: Find the value of a.
- 16M.2.hl.TZ1.12c: Find the equation of the normal to C at the point A.
- 16M.2.hl.TZ1.12d: Find the coordinates of the second point at which the normal found in part (c) intersects C.
- 16M.1.hl.TZ2.4: The function f is defined as f(x) = a{x^2} + bx + c where...
- 16M.1.hl.TZ1.10: Find the x-coordinates of all the points on the curve...
- 16M.2.hl.TZ2.7b: Find the value of k.
- 16N.1.hl.TZ0.9b: Find the equations of the tangents to this curve at the points where the curve intersects the...
- 16N.1.hl.TZ0.11g: Find the value of the curvature of the graph of f at the local maximum point.
- 16N.1.hl.TZ0.11h: Find the value \kappa for x = \frac{\pi }{2} and comment on its meaning with respect to...
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ1.2b: Determine the equation of the tangent to C at the point...
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
- 17N.1.hl.TZ0.11c: Hence or otherwise, find an expression for the derivative of {f_n}(x) with respect to x.
- 17N.1.hl.TZ0.11d: Show that, for n > 1, the equation of the tangent to the curve y = {f_n}(x) at...
- 17N.2.hl.TZ0.10a.i: Show that the x-coordinate of the minimum point on the curve y = f(x) satisfies the...
- 17N.2.hl.TZ0.10a.ii: Determine the values of x for which f(x) is a decreasing function.
- 17N.2.hl.TZ0.10c: Find the coordinates of the point on the graph of f where the normal to the graph is parallel...
- 18M.2.hl.TZ1.9b: Find the equation of the normal to the curve at the point P.
- 18M.2.hl.TZ1.9c: The normal at P cuts the curve again at the point Q. Find the x-coordinate of Q.
- 18M.2.hl.TZ2.11b.i: Find the coordinates of P and Q.
- 18M.2.hl.TZ2.11b.ii: Given that the gradients of the tangents to C at P and Q are m1 and m2 respectively, show that m1...
- 18M.2.hl.TZ2.11c: Find the coordinates of the three points on C, nearest the origin, where the tangent is parallel...
Definition of derivative from first principles as f'\left( x \right) = \mathop {\lim }\limits_{h \to 0} {\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}} .
- 12M.1.hl.TZ2.13a: Using the definition of a derivative as...
- SPNone.1.hl.TZ0.13a: Given that f and its derivative, f' , are continuous for all values in the domain of f , find...
- 16M.2.hl.TZ1.12a: Find the value of a.
- 16M.2.hl.TZ1.12c: Find the equation of the normal to C at the point A.
- 16M.2.hl.TZ1.12d: Find the coordinates of the second point at which the normal found in part (c) intersects C.
- 16M.1.hl.TZ2.4: The function f is defined as f(x) = a{x^2} + bx + c where...
- 16M.1.hl.TZ1.10: Find the x-coordinates of all the points on the curve...
- 16M.2.hl.TZ2.7b: Find the value of k.
- 16N.1.hl.TZ0.9b: Find the equations of the tangents to this curve at the points where the curve intersects the...
- 16N.1.hl.TZ0.11g: Find the value of the curvature of the graph of f at the local maximum point.
- 16N.1.hl.TZ0.11h: Find the value \kappa for x = \frac{\pi }{2} and comment on its meaning with respect to...
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ1.2b: Determine the equation of the tangent to C at the point...
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
- 17N.1.hl.TZ0.11c: Hence or otherwise, find an expression for the derivative of {f_n}(x) with respect to x.
- 17N.1.hl.TZ0.11d: Show that, for n > 1, the equation of the tangent to the curve y = {f_n}(x) at...
- 17N.2.hl.TZ0.10a.i: Show that the x-coordinate of the minimum point on the curve y = f(x) satisfies the...
- 17N.2.hl.TZ0.10a.ii: Determine the values of x for which f(x) is a decreasing function.
- 17N.2.hl.TZ0.10c: Find the coordinates of the point on the graph of f where the normal to the graph is parallel...
- 18M.2.hl.TZ1.9b: Find the equation of the normal to the curve at the point P.
- 18M.2.hl.TZ1.9c: The normal at P cuts the curve again at the point Q. Find the x-coordinate of Q.
- 18M.2.hl.TZ2.11b.i: Find the coordinates of P and Q.
- 18M.2.hl.TZ2.11b.ii: Given that the gradients of the tangents to C at P and Q are m1 and m2 respectively, show that m1...
- 18M.2.hl.TZ2.11c: Find the coordinates of the three points on C, nearest the origin, where the tangent is parallel...
The derivative interpreted as a gradient function and as a rate of change.
- 12M.2.hl.TZ1.1: Given that the graph of y = {x^3} - 6{x^2} + kx - 4 has exactly one point at which...
- 12M.1.hl.TZ2.13a: Using the definition of a derivative as...
- 12M.2.hl.TZ2.6b: Write down the gradient of the curve at x = 1 .
- 15N.1.hl.TZ0.7a: Show that there is no point where the tangent to the curve is horizontal.
- 15N.1.hl.TZ0.7b: Find the coordinates of the points where the tangent to the curve is vertical.
- 16M.2.hl.TZ1.12a: Find the value of a.
- 16M.2.hl.TZ1.12c: Find the equation of the normal to C at the point A.
- 16M.2.hl.TZ1.12d: Find the coordinates of the second point at which the normal found in part (c) intersects C.
- 16M.1.hl.TZ2.4: The function f is defined as f(x) = a{x^2} + bx + c where...
- 16M.1.hl.TZ1.10: Find the x-coordinates of all the points on the curve...
- 16M.2.hl.TZ2.7b: Find the value of k.
- 16N.1.hl.TZ0.9b: Find the equations of the tangents to this curve at the points where the curve intersects the...
- 16N.1.hl.TZ0.11g: Find the value of the curvature of the graph of f at the local maximum point.
- 16N.1.hl.TZ0.11h: Find the value \kappa for x = \frac{\pi }{2} and comment on its meaning with respect to...
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ1.2b: Determine the equation of the tangent to C at the point...
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
- 17N.1.hl.TZ0.11c: Hence or otherwise, find an expression for the derivative of {f_n}(x) with respect to x.
- 17N.1.hl.TZ0.11d: Show that, for n > 1, the equation of the tangent to the curve y = {f_n}(x) at...
- 17N.2.hl.TZ0.10a.i: Show that the x-coordinate of the minimum point on the curve y = f(x) satisfies the...
- 17N.2.hl.TZ0.10a.ii: Determine the values of x for which f(x) is a decreasing function.
- 17N.2.hl.TZ0.10c: Find the coordinates of the point on the graph of f where the normal to the graph is parallel...
- 18M.2.hl.TZ1.9b: Find the equation of the normal to the curve at the point P.
- 18M.2.hl.TZ1.9c: The normal at P cuts the curve again at the point Q. Find the x-coordinate of Q.
- 18M.2.hl.TZ2.11b.i: Find the coordinates of P and Q.
- 18M.2.hl.TZ2.11b.ii: Given that the gradients of the tangents to C at P and Q are m1 and m2 respectively, show that m1...
- 18M.2.hl.TZ2.11c: Find the coordinates of the three points on C, nearest the origin, where the tangent is parallel...
Finding equations of tangents and normals.
- 12M.1.hl.TZ1.9: The curve C has equation 2{x^2} + {y^2} = 18. Determine the coordinates of the four points on...
- 12M.2.hl.TZ1.11d: Find the coordinates of the point of intersection of the normals to the graph at the points P and Q.
- 12M.2.hl.TZ2.6c: Find the equation of the normal to the curve at x = 1 .
- 08M.2.hl.TZ1.13: A family of cubic functions is defined as...
- 08M.1.hl.TZ2.8: A normal to the graph of y = \arctan (x - 1) , for x > 0, has equation...
- 08N.1.hl.TZ0.6: Find the equation of the normal to the curve 5x{y^2} - 2{x^2} = 18 at the point (1, 2) .
- 11M.1.hl.TZ2.11b: The tangent to C at the point P(1, 2) cuts the x-axis at the point T. Determine the coordinates...
- 11M.1.hl.TZ2.11c: The normal to C at the point P cuts the y-axis at the point N. Find the area of triangle PTN.
- 09M.1.hl.TZ1.7: Consider the functions f and g defined by f(x) = {2^{\frac{1}{x}}} and...
- 09N.1.hl.TZ0.12: A tangent to the graph of y = \ln x passes through the origin. (a) Sketch the graphs of...
- SPNone.2.hl.TZ0.13d: Find the equation of the normal to the graph of f where x = 0.75 , giving your answer in the form...
- 13M.1.hl.TZ1.7: A curve is defined by the equation 8y\ln x - 2{x^2} + 4{y^2} = 7. Find the equation of the...
- 10M.1.hl.TZ2.8: The normal to the curve x{{\text{e}}^{ - y}} + {{\text{e}}^y} = 1 + x, at the point (c,...
- 10N.1.hl.TZ0.13: Consider the curve y = x{{\text{e}}^x} and the line \(y = kx,{\text{ }}k \in...
- 10N.2.hl.TZ0.4: Find the equation of the normal to the curve {x^3}{y^3} - xy = 0 at the point (1, 1).
- 10N.2.hl.TZ0.10: The line y = m(x - m) is a tangent to the curve (1 - x)y = 1. Determine m and the...
- 13M.1.hl.TZ2.5b: Find the equation of the tangent to C at the point \left( {\frac{\pi }{2},0} \right).
- 11N.1.hl.TZ0.13a: Find the equation of the tangent to C at the point (2, e).
- 09M.2.hl.TZ1.12: (a) If A, B and C have x-coordinates a\frac{\pi }{2}, b\frac{\pi }{6} and...
- 14M.1.hl.TZ1.11d: The graph of y = {\text{ }}f(x) crosses the x-axis at the point A. Find the equation of...
- 14M.2.hl.TZ1.10d: Find the equation of the line {L_2}.
- 14M.2.hl.TZ2.10b: Find the equation of the normal to the curve at the point (1, 1).
- 13N.2.hl.TZ0.13a: (i) Explain why the inverse function {f^{ - 1}} does not exist. (ii) Show that the...
- 14M.2.hl.TZ1.10b: (i) Find f'(x). (ii) Show that the curve has exactly one point where its tangent is...
- 14M.2.hl.TZ1.10c: Find the equation of {L_1}, the normal to the curve at the point where it crosses the y-axis.
- 14N.1.hl.TZ0.11c: The graph of y = g(x) intersects the x-axis at the point Q. Show that the equation...
- 15M.2.hl.TZ1.9: Find the equation of the normal to the curve...
- 15M.2.hl.TZ2.11b: Find the equation of the normal to the curve at the point (6,{\text{ }}1).
- 15N.3ca.hl.TZ0.5a: Show that the tangent to the curve y = f(x) at the point (1,{\text{ }}0) is normal to the...
- 15N.1.hl.TZ0.4b: Determine the equation of the normal to the curve at the point x = 3 in the form...
- 16M.2.hl.TZ1.12a: Find the value of a.
- 16M.2.hl.TZ1.12c: Find the equation of the normal to C at the point A.
- 16M.2.hl.TZ1.12d: Find the coordinates of the second point at which the normal found in part (c) intersects C.
- 16M.1.hl.TZ2.4: The function f is defined as f(x) = a{x^2} + bx + c where...
- 16M.1.hl.TZ1.10: Find the x-coordinates of all the points on the curve...
- 16M.2.hl.TZ2.7b: Find the value of k.
- 16N.1.hl.TZ0.9b: Find the equations of the tangents to this curve at the points where the curve intersects the...
- 16N.1.hl.TZ0.11g: Find the value of the curvature of the graph of f at the local maximum point.
- 16N.1.hl.TZ0.11h: Find the value \kappa for x = \frac{\pi }{2} and comment on its meaning with respect to...
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ1.2b: Determine the equation of the tangent to C at the point...
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
- 17N.1.hl.TZ0.11c: Hence or otherwise, find an expression for the derivative of {f_n}(x) with respect to x.
- 17N.1.hl.TZ0.11d: Show that, for n > 1, the equation of the tangent to the curve y = {f_n}(x) at...
- 17N.2.hl.TZ0.10a.i: Show that the x-coordinate of the minimum point on the curve y = f(x) satisfies the...
- 17N.2.hl.TZ0.10a.ii: Determine the values of x for which f(x) is a decreasing function.
- 17N.2.hl.TZ0.10c: Find the coordinates of the point on the graph of f where the normal to the graph is parallel...
- 18M.2.hl.TZ1.9b: Find the equation of the normal to the curve at the point P.
- 18M.2.hl.TZ1.9c: The normal at P cuts the curve again at the point Q. Find the x-coordinate of Q.
- 18M.2.hl.TZ2.11b.i: Find the coordinates of P and Q.
- 18M.2.hl.TZ2.11b.ii: Given that the gradients of the tangents to C at P and Q are m1 and m2 respectively, show that m1...
- 18M.2.hl.TZ2.11c: Find the coordinates of the three points on C, nearest the origin, where the tangent is parallel...
Identifying increasing and decreasing functions.
- 12M.1.hl.TZ1.12a: Show that f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}} and deduce that f...
- 14M.3ca.hl.TZ0.2a: Consider the functions f(x) = {(\ln x)^2},{\text{ }}x > 1 and...
- 14N.1.hl.TZ0.11e: A region R is bounded by the graphs of y = g(x), the tangent T and the line...
- 15M.1.hl.TZ2.4a: Determine the values of x for which f(x) is a decreasing function.
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
The second derivative.
- SPNone.1.hl.TZ0.5b: Show that f''(0) = 0 .
- 15N.3ca.hl.TZ0.2a: Show that f''(x) = 2\left( {f'(x) - f(x)} \right).
- 15N.2.hl.TZ0.13a: Find f''(x).
- 17M.1.hl.TZ2.9c: By finding g'(x) explain why g is an increasing function.
- 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \left( {1,{\text{ }}\sqrt 3 } \right).
Higher derivatives.
- 10N.1.hl.TZ0.12b: Consider the...
- 11N.1.hl.TZ0.6: Given that y = \frac{1}{{1 - x}}, use mathematical induction to prove that...
- 15N.1.hl.TZ0.8b: Consider f(x) = \sin (ax) where a is a constant. Prove by mathematical induction that...
- 16M.1.hl.TZ2.11c: (i) Find \frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}}. (ii) Find the values of...
- 16N.1.hl.TZ0.11b: Show that \frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 2{{\text{e}}^x}\cos x.
- 17N.2.hl.TZ0.11a.i: Determine an expression for f’(x) in terms of x.
- 17N.2.hl.TZ0.11a.ii: Sketch a graph of y = f’(x) for 0 \leqslant x < \frac{\pi }{2}.
- 17N.2.hl.TZ0.11a.iii: Find the x-coordinate(s) of the point(s) of inflexion of the graph of y = f(x), labelling...