Problem

3. $\displaystyle f(x)=\begin{cases}|x|-1, & \text{for } -1\le x\le 3,\\ (x-6)^2-4, & \text{for } 3<x\le 10.\end{cases}$ $\displaystyle g(x)=\int_0^x f(t)\,dt$, for $-1\le x\le 10$.

(a) Choose correct statement(s) about $g(x)$: $\underline{\quad(8)\quad}$

i. $g(x)$ is discontinuous at $x=3$.

ii. $g(x)$ is not differentiable at $x=3$.

iii. $g(x)$ is differentiable at $x=0$ and $g'(0)=-1$.

iv. $g(x)<0$ for $-1\le x<0$.

(b) The local minimum values of $g(x)$ occur at $x=\underline{\quad(9)\quad}$.

(c) The $x$-coordinates of points of inflection for $y=g(x)$ are $\underline{\quad(10)\quad}$.