AP® Calculus AB-BC

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Moderate

Extrema Statements

APCALC-RRO1C8

$f( x ) =\cfrac { { x }^{ 5 } }{ 10 } -\cfrac { { x }^{ 4 } }{ 6 } -\cfrac { { 11 }x^{ 3 } }{ 12 } +\cfrac { { 3x }^{ 2 } }{ 2 } +7x-\cfrac { 3 }{ 4 } $

Which of the following is true for the derivative of the above curve?

A

It has four inflection points at $2, \ \cfrac{1}{2},\ 0 $ and $-\cfrac{3}{2}$.

B

It has a maxima at $2$ and minima at $1,2$ and $-\cfrac{3}{2}$.

C

It has minima at $\cfrac{1}{2},\ 2$ and maxima at $-\cfrac{3}{2}$.

D

It has minima at $2,\ -\cfrac{3}{2}$ and maxima at $\cfrac{1}{2}$.