The sum of two positive numbers is 5. What is the value of the larger number if the product of the smaller number and the cube of the larger is a maximum? a. 5 b. 15/4 c. 5/4 d.1 e.0
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So a + b = 5 and some f(x) = a(b)^3. a = 5-b $\displaystyle f(x) = (5-b)(b^3) = 5b^3 - b^4$ Max occurs at f'(x) = 0 $\displaystyle 15b^2 - 4b^3 = 0$ $\displaystyle b^2(15-4b) = 0$ b = 0, 15/4 f''(15/4) < 0 Answer 15/4
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