The family of bell-shaped curves occurs in probability and statistics, where it is called the normal
density function. The constant Âµ is called the mean and the positive constant Ï is called the standard deviation. For simplicity, letâs scale the function so as to remove the factor 1/(Ïâ2Ï and letâs analyze the special case where Âµ = 0. So, we study the function
(a). Find the asymptote, maximum value, and inflection points of f. (b). What role does Ï play in the shape of the curve? (c). Illustrate by graphing four members of this family on the same screen.
f(x) = e =*/2u*)