## Calculus (3rd Edition)

The minimum value is $f(-2)=-44$ and the maximum value is $f(2)=84$
$f'(x)=10x^{4}+10x$ is defined everywhere. The critical points are the solutions of $f'(x)=0$ $10x^{4}+10x= 10x(x^{3}+1)=0$ $\implies x=0$ or $x=-1$ The critical points are $0$ and $-1$. In order to find the maximum and minimum values, we compare the values of the function at the critical points and at the end points. $f(0)=0$ $f(-1)= 2(-1)^{5}+5(-1)^{2}=3$ $f(-2)= 2(-2)^{5}+5(-2)^{2}=-44$ $f(2)= 2(2)^{5}+5(2)^{2}=84$ The minimum value is $f(-2)=-44$ and the maximum value is $f(2)=84$