It is easily verified that the graphs of y = x 2 and y = e x

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It is easily verified that the graphs of y = x2 and y = ex have no points of intersection (for x > 0), and the graphs of y = x3 and y = ex have two points of intersection. It follows that for some real number 2 < p < 3, the graphs of y = xp and y = ex have exactly one point of intersection (for x > 0). Using analytical and/or graphical methods, determine p and the coordinates of the single point of intersection.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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