Question

The function defined by $f\left(x\right)=max\{x^2,(x-1{)}^2,2x(1-x)\}$ for $0<x<1$

• A. is differentiable for all $x$.
• B. is differentiable for all $x$ except at one point.
• C. is differentiable for all $x$ except at two points.
• D. is not differentiable at more than two points.

Answer 1

The correct option is C is differentiable for all $x$ except at two points.


From the above graph, clearly there are two such points where $f\left(x\right)$ is not differentiable.