$4.(20$ points$)$ Consider the function $\backslash ($ y$=-$e$^\{-$x$^\{2\}\}\backslash )$

$($a$)$ Find the critical value$($s$)$ and stationary point$($s$).$

$($b$)$ Determine whether the points found in part a are minima or maxima or something else.

$($c$)$ Draw the function and identify the stationary point$($s$)$ and other critical points. Use enough points to draw it with enough accuracy.

$($d$)$ Is this function continuous? Is its first derivative continuous? Just give an intuitive answer by looking at the function.