Chapter 4.3, Problem 50E

(a)

To determine

To find: The asymptote, maximum value and inflection point of the given function.

(b)

To determine

To explain: The role of standard deviation $\sigma$ in the curve $y=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{-{\left(x-\mu \right)}^2}{2{\sigma }^2}}$.

(c)

To determine

To sketch: The graph of four member of family of bell shaped curves $y=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{-{\left(x-\mu \right)}^2}{2{\sigma }^2}}$.