I am a little confused on how to find the absolute max and min without using a calculator. I know I have to find the derivative of this function and find critical values, but I'm not finding any critical values. I know that the max value of this function in the given interval is $(-5,5)$, but I cannot find the minimum. Any suggestions?
Best Answer
The critical values are the x values where $n'$ is either $0$ or undefined. There is no point at which $n'(x)=0$, but $n'(3)$ is undefined. Therefore, the maximum and minimum values can only occur when $x\in\{-5,3,5\}$. Since $n(-5)=5$, $n(3)=-3$, and $n(5)=-1$, the absolute maximum is $5$ and the absolute minimum is $-3$.