DP Mathematics SL Questionbank
Local maximum and minimum points.
Description
[N/A]Directly related questions
- 18M.2.sl.TZ1.10b.ii: For the graph of \(f\), write down the period.
- 18M.2.sl.TZ1.10e: Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
- 18M.2.sl.TZ1.10d: Find the maximum speed of the ball.
- 18M.2.sl.TZ1.10c: Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).
- 18M.2.sl.TZ1.10b.i: For the graph of \(f\), write down the amplitude.
- 18M.2.sl.TZ1.10a: Find the coordinates of A.
- 18M.1.sl.TZ1.8c: Find the values of x for which the graph of f is concave-down.
- 18M.1.sl.TZ1.8b: The graph of f has a point of inflexion at x = p. Find p.
- 18M.1.sl.TZ1.8a: Find f (x).
- 17M.2.sl.TZ2.8d: Let \(R\) be the region enclosed by the graph of \(f\) , the \(x\)-axis, the line \(x = b\) and...
- 17M.2.sl.TZ2.8c.ii: Find the the rate of change of \(f\) at B.
- 17M.2.sl.TZ2.8c.i: Find the coordinates of B.
- 17M.2.sl.TZ2.8b.ii: Write down the rate of change of \(f\) at A.
- 17M.2.sl.TZ2.8b.i: Write down the coordinates of A.
- 17M.2.sl.TZ2.8a: Find the value of \(p\).
- 17M.2.sl.TZ1.10c: Let \(d\) be the vertical distance from a point on the graph of \(h\) to the line \(y = x\)....
- 17M.2.sl.TZ1.10b.ii: Hence, find the area of the region enclosed by the graphs of \(h\) and \({h^{ - 1}}\).
- 17M.2.sl.TZ1.10b.i: Find \(\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} \).
- 17M.2.sl.TZ1.10a.iii: Write down the value of \(k\).
- 17M.2.sl.TZ1.10a.i: Write down the value of \(q\);
- 17M.2.sl.TZ1.10a.ii: Write down the value of \(h\);
- 16M.1.sl.TZ1.9c: The graph of \(f\) is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\)....
- 16M.1.sl.TZ1.9b: Find \(f(x)\), expressing your answer as a single logarithm.
- 16M.1.sl.TZ1.9a: Find the \(x\)-coordinate of P.
- 16N.2.sl.TZ0.10c: (i) Find \(w\). (ii) Hence or otherwise, find the maximum positive rate of change of \(g\).
- 16N.2.sl.TZ0.10b: (i) Write down the value of \(k\). (ii) Find \(g(x)\).
- 16N.2.sl.TZ0.10a: (i) Find the value of \(c\). (ii) Show that \(b = \frac{\pi }{6}\). (iii) Find the...
- 12M.1.sl.TZ2.10a: Use the quotient rule to show that \(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) .
- 12M.1.sl.TZ2.10b: Hence find the coordinates of B.
- 12M.1.sl.TZ2.10c: Given that the line \(y = k\) does not meet the graph of f , find the possible values of k .
- 08N.1.sl.TZ0.6a(i) and (ii): (i) Write down the value of \(f'(x)\) at C. (ii) Hence, show that C corresponds to a...
- 08N.1.sl.TZ0.6b: Which of the points A, B, D corresponds to a maximum on the graph of f ?
- 08M.1.sl.TZ1.8b: Find the x-coordinate of M.
- 08M.2.sl.TZ1.5b: Complete the table, for the graph of \(y = f(x)\) .
- 08M.1.sl.TZ2.10d: Find the value of \(\theta \) when S is a local minimum, justifying that it is a minimum.
- 08M.2.sl.TZ2.9c: Write down the value of r and of s.
- 10M.1.sl.TZ1.8a: Find the coordinates of A.
- 10M.1.sl.TZ1.8b(i), (ii) and (iii): Write down the coordinates of (i) the image of B after reflection in the y-axis; (ii) ...
- 10M.1.sl.TZ2.8a: Use the second derivative to justify that B is a maximum.
- 10M.1.sl.TZ2.8b: Given that \(f'(x) = \frac{3}{2}{x^2} - x + p\) , show that \(p = - 4\) .
- 10M.1.sl.TZ2.8c: Find \(f(x)\) .
- 09N.1.sl.TZ0.5b: There is a minimum value of \(f(x)\) when \(x = - 2\) . Find the value of \(p\) .
- 11M.1.sl.TZ1.5a: Use the quotient rule to show that \(g'(x) = \frac{{1 - 2\ln x}}{{{x^3}}}\) .
- 11M.1.sl.TZ1.5b: The graph of g has a maximum point at A. Find the x-coordinate of A.
- 13N.1.sl.TZ0.10b: There is a minimum on the graph of \(f\). Find the \(x\)-coordinate of this minimum.
- 13N.1.sl.TZ0.10c: Write down the value of \(p\).
- 14N.1.sl.TZ0.9a: Find the \(x\)-coordinate of \(A\).
- 15N.1.sl.TZ0.10a: Explain why the graph of \(f\) has a local minimum when \(x = 5\).
