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Geometric and arithmetic means Given positive numbers x1, …, xn, prove that the geometric mean (x1x2 … xn)1/n is no greater than the arithmetic mean (x1+ … + xn)/n in the following cases.
a. Find the maximum value of xyz, subject to x + y + z = k, where k is a real number and x > 0, y > 0, and z > 0. Use the result to prove that
b. Generalize part (a) and show that
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Calculus: Early Transcendentals (3rd Edition)
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