A Monotone Decrease Constraint

★ 7/10functions Linear Programming Monotonicity AM-GM inequality

Problem

Let $m, n \geqslant 0$ , and suppose

f(x) = \frac{1}{2}(m-2)x^2 + (n-8)x + 1

is decreasing on the interval $\left[\dfrac{1}{2}, 2\right]$ . Find the maximum value of $mn$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Linear Programming, Monotonicity, AM-GM, inequality

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