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, .
Find the possible values of .
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21N.3.AHL.TZ0.1e:
Show that .
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21N.3.AHL.TZ0.1d:
Hence find, and simplify, an expression for .
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21N.3.AHL.TZ0.1f:
Sketch the graph of , 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 .
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22M.1.SL.TZ1.7e.ii:
Find the values of for which the graph of is concave-down. Justify your answer.
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22M.2.AHL.TZ2.12d:
Hence determine the maximum value of in terms of and .
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22M.1.AHL.TZ1.12c.i:
Show that satisfies the equation .
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19M.1.AHL.TZ2.H_8a:
Show that the volume of the cone may be expressed by .
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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 .
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18M.1.AHL.TZ1.H_9b.ii:
The coordinates of B can be expressed in the form B where a, b. Find the value of a and the value of b.
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18M.1.AHL.TZ1.H_9c:
Sketch the graph of 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 , .
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18N.1.AHL.TZ0.H_10b:
Hence, show that , .
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18N.1.AHL.TZ0.H_10c:
Find the -coordinates of A and of C , giving your answers in the form , where , .
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18N.1.AHL.TZ0.H_10d:
Find the area enclosed by the curve and the -axis between B and D, as shaded on the diagram.
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19M.1.AHL.TZ1.H_8a:
Write down the -coordinate of the point of inflexion on the graph of .
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19M.1.AHL.TZ1.H_8b:
find the value of .
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19M.1.AHL.TZ1.H_8c:
find the value of .
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19M.1.AHL.TZ1.H_8d:
Sketch the curve , 0 ≤ ≤ 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 in terms of .
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19N.1.SL.TZ0.S_8b:
Find an expression for in terms of .
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19N.1.SL.TZ0.S_8c:
Find .
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19N.1.SL.TZ0.S_8d.i:
Find the value of for which 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 showing clearly any intercepts with the axes.
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17M.1.AHL.TZ1.H_12e.i:
Show that the graph of is concave up for .