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Let f(x) = x3 + 3x2 − 9x − 27 . The first and second derivatives...

Let f(x) = x3 + 3x2 − 9x − 27 . The first and second derivatives of f are given below.

f(x) = x3 + 3x2− 9x − 27 = (x − 3)(x + 3)2

f '(x) = 3x2 + 6x − 9 = 3(x − 1)(x + 3)

f ''(x) = 6x + 6 = 6(x + 1)

a.) Find the x-intercepts on the graph of f.

b.)Find the critical points of f.

c.) Identify the possible inflection points of f.

d.) Determine the location and value of any local maxima and local minima of f, if they exist.

e.) Determine the end behavior and locate any horizontal asymptotes on the graph of f if they exist.

Math   Calculus   
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