Question: The family of bell-shaped curves occurs

The family of bell-shaped curves occurs in probability and statistics, where it is called the normal density function. The constant µ is called the mean and the positive constant σ is called the standard deviation. For simplicity, let’s scale the function so as to remove the factor 1/(σ√2π and let’s analyze the special case where µ = 0. So, we study the function

(a). Find the asymptote, maximum value, and inflection points of f. (b). What role does σ play in the shape of the curve? (c). Illustrate by graphing four members of this family on the same screen.