Stationary point and convexity

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Problem

For $f(w)=w^2-4w+5$ , find all stationary points, determine convexity, and give the global minimum value.

Reveal answer or reference solution

Since $f'(w)=2w-4$ , the only stationary point is $w=2$ . Because $f''(w)=2>0$ everywhere, $f$ is strictly convex and $w=2$ is the unique global minimizer. The minimum value is $f(2)=1$ .

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Stationary point and convexity

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