Let $$f(x)=\begin{cases} 0 & \text{ if } x < 0 \\ x & \text{ if } 0 \le x \le 1 \\ 2-x & \text{ if } 1 < x \le 2 \\ 0 & \text{ if } x > 2 \end{cases}$$ and $$g(x)=\int_{0}^{\,x} {f(t)}\,dt$$

(a) Find an expression for $g$.

For $x < 0,$ $g(x)=$

For $0 \le x \le 1,$ $g(x)=$

For $1 < x \le 2,$ $g(x)=$

For $x > 2,$ $g(x)=$

(b) Where is $f$ not differentiable?

List the values of $x$ in increasing order. Type an upper-case "N" in any unused answer fields. If $f$ is differentiable everywhere, type an upper-case "N" in every blank.

Smallest value of $x$ is

Next smallest value of $x$ is

Next smallest value of $x$ is

(c) Where is $g$ not differentiable?

List the values of $x$ in increasing order. Type an upper-case "N" in any unused answer fields. If $g$ is differentiable everywhere, type an upper-case "N" in every blank.

Smallest value of $x$ is

Next smallest value of $x$ is

Next smallest value of $x$ is