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Second Derivative and Points of Inflection

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The second derivatives of the twice-differentiable functions ff, gg, and hh are given by:

f′′(x)=x(x−1)2(x+2)3\displaystyle f''(x) = x(x - 1)^2 (x + 2)^3

g′′(x)=x(x−1)2(x+2)3+1\displaystyle g''(x) = x(x - 1)^2 (x + 2)^3 + 1

h′′(x)=x(x−1)2(x+2)3−1\displaystyle h''(x) = x(x - 1)^2 (x + 2)^3 - 1

Which of the functions ff, gg, and hh have a graph with exactly two points of inflection?

A

ff and gg only

B

gg only

C

hh only

D

ff, gg, and hh

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