Question

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

Answer 1

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]}