Extrema from an ODE Condition

★ 7/10functions Extrema calculus Monotonicity

Problem

Let $f(x)$ satisfy

x^2f'(x)+2xf(x)=\frac{\mathrm e^x}x,\qquad f(2)=\frac{\mathrm e^2}8.

For $x>0$ , determine, with justification, whether $f(x)$ has a local maximum and/or a local minimum.

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity

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