\text { For the following function } f(x)=x e^{-x^{2}} a. Find the intervals where the function is increasing/decreasing. b. Find local max/min values. c. Find the intervals where the function is concave upward/downward. d. Find inflection point(s), if any. e. Sketch the graph of the function y = f (x). • The Domain of the function f (x) is the set of all real numbers. \text { - } \lim _{x \rightarrow \infty} f(x)=0 \text { and } \lim _{x \rightarrow-\infty} f(x)=0 \text {. }