Question

How do you find the exact relative maximum and minimum of the polynomial function of `f (x) = x^3 - 6x^2 - 15x + 11`?

Answer 1

See below.

Explanation:

`f'(x) = 3x^2-12x-15 = 3(x^2-4x-5) = 3(x+1)(x-5)`

The critical numbers for `f` are `-1` and `5`.

`f''(x) = 6x-12` therefore

`f''(-1) < 0` so `f(-1) = 19` is a relative maximum.

`f''(5) > 0` so `f(5) = -89` is a relative minimum.