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

Jan 4, 2016

$\left(- 1 , 14\right)$

#### Explanation:

The extrema occur when $f ' \left(x\right) = 0$ or when $f ' \left(x\right)$ is undefined.

To find $f ' \left(x\right)$, use the power rule.

$f ' \left(x\right) = 2 x + 2$

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

$f ' \left(x\right)$ is never undefined, thus the only extrema is at $x = - 1$.

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