A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$. If the function ' $f$ ' is differentiable at $x=0$, then $f$ is

The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is

A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect?

Let $f(x)$ be continuous on $[0,5]$ and differentiable in $(0,5)$. If $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq \frac{1}{5}$ for all $x$ in $(0,5)$, then $\forall x$ in $[0,5]$