Question

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

Answer 1

Find `f'(x)`, find the critical number for `f`, test the critical numbers.

`f'(x)=28x(x^2-16)`

`f'(x)` never fails to exist.

`f'(x)=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(-4)=f(4)=0` is a relative minimum.

`f(0) = 7 (16^2) = 1792` is a relative maximum.