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Moderate

Critical Numbers for Function with Rational Derivative

APCALC-OZP49G

What are the critical numbers for the function $f(x)$ that is defined for all real numbers $x$ if:

$$f^{ \prime }(x)=\cfrac { ({ x }^{ 2 }-16) }{ ({ 2x }^{ 2 }+7x-15) } $$

A

$x=4,-4,\ \cfrac{3}{2},-5$

B

$x=4, -4$

C

$x= \cfrac{3}{2},-5$

D

$x=4,-4, -\cfrac{3}{2}, \ 5$