For the function $f(x) = e^{2x}+e^{-x}$ defined on the interval $\left(-\infty ,1\right]$, find all intervals where the function is strictly increasing or strictly decreasing. Your intervals should be as large as possible.
$f$ is strictly increasing on
$f$ is strictly decreasing on
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)

Find and classify all local max's and min's. (For the purposes of this exercise we'll call an endpoint $c$ a "local max" if $f(c)\geq f(x)$ whenever $x$ is near $c$ on the left or on the right. Similarly, we'll call it a "local min" if $f(c)\leq f(x)$ whenever $x$ is near $c$ on the left or right.)

Enter your maxima and minima as comma-separated xvalue,classification pairs. For example, if you found that $x = -2$ was a local minimum and $x = 3$ was a local maximum, you should enter (-2,min), (3,max). If there were no maximum, you must drop the parentheses and enter -2,min.