$f$ is twice differentiable, $f + 2 f^{'} + f^{''} \geq 0$ , prove the following

Hint Let $g(x)=f(x)e^x$. Then $$g''=(f+2f'+f'')e^x \geq 0 \,.$$

That means that $g$ is.... How does this solve the problem?


HINT: If not, $f$ must have a maximum in the interior of the interval.

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Calculus

Derivatives

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