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

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Answer 1 · 2015-04-26T14:22:51

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.