Chapter 4.2, Problem 79ES

Function similar to $f\left(x\right)=\frac{1}{\sqrt{2\pi }}{e}^{-x^2/2}$ arise in a wide variety of statistical problems.

(a) Use the first derivate test to show that $f$ has a relative maximum at $x=0,$ and confirm this by using a graphing utility of graph $f$ .

(b) Sketch the graph of $f\left(x\right)=\frac{1}{\sqrt{2\pi }}{e}^{-{\left(x-\mu \right)}^2/2}$ where $\mu$ is a constant, and label the coordinates of the relative extrema.