2.99
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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 Ïƒ is called the standard deviation. For simplicity, letâ€™s scale the function so as to remove the factor 1/(Ïƒâˆš2Ï€ and letâ€™s 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 Ïƒ play in the shape of the curve?
(c). Illustrate by graphing four members of this family on the same screen.

f(x) = e =*/2u*)