# Thread: Prove norm of continuously differentiable function - repost from "urgent"

1. ## Prove norm of continuously differentiable function - repost from "urgent"

Hello everyone, I might be breaking all rules by reposting my question here as well but the "urgent homework" forum did not quite seem to be the right place.

Can someone prove that for any continuously differentable function on :

Yes I know I am supposed to do it and I assume Cauchy-Schwarz is somehow involved but I cannot make out the details

Best regards and thanks,
Thomas

2. Cauchy–Schwarz in $\mathbb{R}^2$ tells you that

\begin{aligned}|f(t)\cos t-f'(t)\sin t| &= |(f(t),f'(t))\mathbf{\cdot}(\cos t,-\sin t)|\\ &\leqslant
\left(|f(t)|^2+|f'(t)|^2\right)^{1/2}\left(\cos^2t+\sin^2t\right)^{1/2}. \end{aligned}