DP Mathematics: Analysis and Approaches Questionbank

SL 5.7—The second derivative
Description
[N/A]Directly related questions
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21N.1.SL.TZ0.9c.i:
Find the value of x where the graph of f has a local minimum. Justify your answer.
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21N.1.SL.TZ0.9a:
Find all the values of x where the graph of f is increasing. Justify your answer.
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21N.1.SL.TZ0.9b:
Find the value of x where the graph of f has a local maximum.
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21N.1.SL.TZ0.9c.ii:
Find the values of x where the graph of f has points of inflexion. Justify your answer.
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21N.1.SL.TZ0.9d:
The total area of the region enclosed by the graph of f', the derivative of f, and the x-axis is 20.
Given that f(p)+f(t)=4, find the value of f(0).
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21N.3.AHL.TZ0.1b:
Show that (f(t))2+(g(t))2=f(2t).
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21N.3.AHL.TZ0.1c.i:
f(iu).
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21N.3.AHL.TZ0.1c.ii:
g(iu).
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21N.3.AHL.TZ0.1a:
Verify that u=f(t) satisfies the differential equation d2udt2=u.
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21N.3.AHL.TZ0.1g:
The hyperbola with equation x2-y2=1 can be rotated to coincide with the curve defined by xy=k, k∈ℝ.
Find the possible values of k.
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21N.3.AHL.TZ0.1e:
Show that (f(t))2-(g(t))2=(f(iu))2-(g(iu))2.
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21N.3.AHL.TZ0.1d:
Hence find, and simplify, an expression for (f(iu))2+(g(iu))2.
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21N.3.AHL.TZ0.1f:
Sketch the graph of x2-y2=1, stating the coordinates of any axis intercepts and the equation of each asymptote.
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22M.1.SL.TZ1.7e.i:
Write down the value of a.
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22M.1.SL.TZ1.7e.ii:
Find the values of x for which the graph of f is concave-down. Justify your answer.
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22M.2.AHL.TZ2.12d:
Hence determine the maximum value of dPdt in terms of k and N.
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22M.1.AHL.TZ1.12c.i:
Show that g(x) satisfies the equation g''(x)=2(g'(x)-g(x)).
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19M.1.AHL.TZ2.H_8a:
Show that the volume of the cone may be expressed by V=π3(2Rh2−h3).
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19M.1.AHL.TZ2.H_8b:
Given that there is one inscribed cone having a maximum volume, show that the volume of this cone is 32πR381.
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18M.1.AHL.TZ1.H_9b.ii:
The coordinates of B can be expressed in the form B(2a,b×2−3a) where a, b∈Q. Find the value of a and the value of b.
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18M.1.AHL.TZ1.H_9c:
Sketch the graph of y=f(x) showing clearly the position of the points A and B.
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18N.1.AHL.TZ0.H_10a:
Use integration by parts to show that ∫excos2xdx=2ex5sin2x+ex5cos2x+c, c∈R.
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18N.1.AHL.TZ0.H_10b:
Hence, show that ∫excos2xdx=ex5sin2x+ex10cos2x+ex2+c, c∈R.
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18N.1.AHL.TZ0.H_10c:
Find the x-coordinates of A and of C , giving your answers in the form a+arctanb, where a, b∈R.
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18N.1.AHL.TZ0.H_10d:
Find the area enclosed by the curve and the x-axis between B and D, as shaded on the diagram.
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19M.1.AHL.TZ1.H_8a:
Write down the x-coordinate of the point of inflexion on the graph of y=f(x).
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19M.1.AHL.TZ1.H_8b:
find the value of f(1).
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19M.1.AHL.TZ1.H_8c:
find the value of f(4).
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19M.1.AHL.TZ1.H_8d:
Sketch the curve y=f(x), 0 ≤ x ≤ 5 indicating clearly the coordinates of the maximum and minimum points and any intercepts with the coordinate axes.
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19N.1.SL.TZ0.S_8a:
Write down an expression for y in terms of x.
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19N.1.SL.TZ0.S_8b:
Find an expression for V in terms of x.
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19N.1.SL.TZ0.S_8c:
Find dVdx.
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19N.1.SL.TZ0.S_8d.i:
Find the value of x for which V is a maximum.
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19N.1.SL.TZ0.S_8d.ii:
Justify your answer.
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19N.1.SL.TZ0.S_8e:
Find the maximum volume.
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17M.1.AHL.TZ1.H_12e.ii:
Sketch the graph of y=q(x) showing clearly any intercepts with the axes.
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17M.1.AHL.TZ1.H_12e.i:
Show that the graph of y=q(x) is concave up for x>1.