Consider the cubic polynomial f(x) = x(x - a)(x - b), where 0 a b.

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Consider the cubic polynomial f(x) = x(x - a)(x - b), where 0 ≤ a ≤ b.

a. For a fixed value of b, find the functionF(a) = Sf(x) dx. For what value of a (which depends on b) is F(a) = 0?

b. For a fixed value of b, find the function A(a) that gives the area of the region bounded by the graph of f and the x-axis between x = 0 and x = b. Graph this function and show that it has a minimum at a = b/2. What is the maximum value of A(a), and where does it occur (in terms of b)?

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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