Question

What are the extrema of `f(x)=x^2+2x+15` on `[-oo,oo]`?

Answer 1

`(-1,14)`

Explanation:

The extrema occur when `f'(x)=0` or when `f'(x)` is undefined.

To find `f'(x)`, use the power rule.

`f'(x)=2x+2`

`f'(x)=0` when `2x+2=0`, so there's an extrema at `x=-1`.

`f'(x)` is never undefined, thus the only extrema is at `x=-1`.

graph{x^2+2x+15 [-10, 10, -5, 30.46]}