The cross-sectional area of a beam cut from a log with radius 1 foot is given by

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The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function

4xV1 – x², 1 -. A(x)


where x represents the length, in feet, of half the base of the beam. See the figure.

A(x) 3 4х /1 — х2 – x х


(a) Find the domain of A.

(b) Use a graphing utility to graph the function A = A(x).

(c) Create a TABLE with Tb1 Start = 0 and ΔTb1 = 0.1 for 0 ‰¤ x ‰¤ 1. Which value of x maximizes the cross- sectional area? What should be the length of the base of the beam to maximize the cross-sectional area?

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Precalculus

ISBN: 978-0321716835

9th edition

Authors: Michael Sullivan

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