Is it true that if $0< f(x)$ is a continuously differentiable function on $\mathbb R$ with $\int_{-\infty}^{\infty}|f(x)|^{2}dx<\infty$ then $|f(x)|$ must be bounded above on $\mathbb R$?
Bounded function on $\mathbb R$
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calculus
real-analysis
functional-analysis