Chapter 4.3, Problem 53E

(a)

To determine

To find: The vertical and horizontal asymptotes of the function $f\left(x\right)=e^{-x^2}$.

(b)

To determine

To find: On which intervals the function $f\left(x\right)=e^{-x^2}$ is increasing or decreasing.

(c)

To determine

To find: The local maximum and minimum values of the function $f\left(x\right)=e^{-x^2}$.

(d)

To determine

To find: The intervals of concavity and the inflection points of the function $f\left(x\right)=e^{-x^2}$.

(e)

To determine

To sketch: The graph of the function f.