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

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Answer 1 · 2016-01-04T06:36:30

$(-1,14)$

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]}

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