The question is
Give an example of a function which is continuous on $[0,1]$, differentiable on $(0,1)$ and not differentiable at the end points. Justify your answer.
Please give me the function with justification.
Give an example of a function which is continuous on $[0,1]$, differentiable on $(0,1)$ and not differentiable at the end points.
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calculus
real-analysis
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3$\sqrt{\frac{1}{4}-\left(x-\frac{1}{2}\right)^2}$. Half a circle. The tangent lines at the endpoints are orthogonal to the $x$-axis. – 2017-02-25
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0Similarly $\sqrt{\sin \frac x\pi}$ – 2017-02-25
1 Answers
4
$\sqrt{x(1-x)}$
Like $\sqrt{x}$ but symmetric.
Note that $(x^{1/2})' =\frac12 x^{-1/2} $ so the derivative at $0$ does not exist.