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

1 Answer
Apr 26, 2015

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.