# How do you find the relative maxima and minima of the function f(x)= 7(x^2 - 16)^2?

Apr 26, 2015

Find $f ' \left(x\right)$, find the critical number for $f$, test the critical numbers.

$f ' \left(x\right) = 28 x \left({x}^{2} - 16\right)$

$f ' \left(x\right)$ never fails to exist.

$f ' \left(x\right) = 0$ at $0 , 4 , - 4$

Since the domain if $f$ is all real numbers, those 3 numbers are all critical numbers.

Use either the first or second derivative test to see that

$f \left(- 4\right) = f \left(4\right) = 0$ is a relative minimum.

$f \left(0\right) = 7 \left({16}^{2}\right) = 1792$ is a relative maximum.