I was asked by one of my student to prove the following problem:
Prove that the graph of the continous function $ y=f(x) = \left\{ \begin{array}{ll} \sqrt{x}\cos\left(\pi/x\right) & \quad 0
shown as
is a nonrectible curve $C$.
I think, I should prepare a solid judgment based on discontinuity of $f'(x)$. What do you think? Please make me sure. Thanks for your time.