What are the extrema of f(x) = 64-x^2 on the interval [-8,0]?

1 Answer
Dec 30, 2015

Find the critical values on the interval (when f'(c)=0 or does not exist).

f(x)=64-x^2

f'(x)=-2x

Set f'(x)=0.

-2x=0

x=0

And f'(x) is always defined.

To find the extrema, plug in the endpoints and the critical values. Notice that 0 fits both of these criteria.

f(-8)=0larr"absolute minimum"

f(0)=64larr"absolute maximum"

graph{64-x^2 [-8, 0, -2, 66]}