Question: For the function \[f(x)=x\cdot {{e}^{x}}\] find the following: (10 points each question)

a. Horizontal or vertical asymptotes, if they exist.

b. Points of maximum or minimum, and the function’s value at these points.

c. Inflection points and the value of the function at these points.

d. Describe the behavior of the graph of this function.