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Maximum value

Source: Nigeria Olympiad senior mathematics round 2 2020 problem 5

January 19, 2020
algebra

Problem Statement

Given that f(x)=(3+2x)3(4−x)4f(x)=(3+2x)^3(4-x)^4 on the interval −32<x<4\frac{-3}{2}<x<4. Find the a. Maximum value of f(x)f(x) b. The value of xx that gives the maximum in (a).
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