Answer
$y$ has no maximum or minimum values at all.
Work Step by Step
$$y=e^x-e^{-x}$$
1) Find all the critical points of the function:
- Find $y'$: $$y'=e^x(x)'-e^{-x}(-x)'$$ $$y'=e^x+e^{-x}$$
- As both $e^x$ and $e^{-x}$ are $\gt0$ for all $x$, there is no value of $x$ for which $y'=0$
- There is also no value of $x$ for which $y'$ is not defined.
So function $y$ has no critical points.
2) Since function $y$ has no critical points and there are also no predefined domains to have the endpoints, we can conclude that $y$ has no maximum or minimum values at all.
This can be seen in the graph of $y$, which is a constantly increasing curve as $x$ increases rightward.
