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AP® Calculus AB-BC

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Moderate

Relative Extrema of a Function

APCALC-FL1VES

Find the locations and type of all relative extrema for the function,

$$f( x ) ={ 2x }^{ 3 }+{ 4x }^{ 2 }-8x-11$$

A

$f(x)$ has a relative maximum at $x=-\cfrac{1}{2}$

B

$f(x)$ has a relative minimum at $x=\cfrac{2}{3}$

C

$f(x)$ has a relative maximum at $-\cfrac{2}{3}$ and a relative minimum at $x=4$.

D

$f(x)$ has a relative maximum at $x=-2$ and a relative minimum at $x=\cfrac{2}{3}$