A Minimum That Stays Positive

★ 8/10Extrema calculus Monotonicity Logarithms

Problem

The function

f(x) = a\ln x - \frac{1}{2}x^2 + bx

has a local minimum, and for every value of $b$ for which this happens, that local minimum is positive. Find the minimum possible value of $a$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, Monotonicity, Logarithms

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