Check Differentiability of Absolute Function at any given point | Calculus

Question:

For what value of $x$, $f(x)=|2x-7|$ is not differentiable.

Answer:

We need to find the input value for which the function will not be differentialable. In other words, the point where the function has a break or sharp edge (cusp; there are infinte many tangents available at that point) $$f(x)=\{\begin{array}{ll}2x-7& x\le {\displaystyle \frac{7}{2}}\\ 7-2x& x<{\displaystyle \frac{7}{2}}\end{array}$$ Hence, for the value $x=\frac{7}{2}$, the function is not differentialable.