Question

What are the extrema of `f(x)=x^2-192x+8` on `x in[-4,9]`?

Answer 1

The minimum is `f(9)`, and the maximum is `f(-4)`.

Explanation:

`f'(x) = 2x-192`, so there are no critical numbers for `f` in the interval chosen.

Therefore, The minimum and maximum occur at the endpoints.

`f(-4) = 16+192(4)+8` is clearly a positive number and `f(9)=81-192(9)+4` is clearly negative.

So, the minimum is `f(9)`, and the maximum is `f(-4)`.