Let $g(x)=\int_{0}^{\,x} {f(t)}\,dt,$ where $f$ is the function whose graph is shown below.

(a) At what values of $x$ do the local maximum values of $g$ occur?

List all values of $x$ in increasing order. If an answer field is unused, type an upper-case "N" in it.

Smallest local maximum value at $x =$

Next smallest local maximum value at $x =$

Next smallest local maximum value at $x =$

(b) At what values of $x$ do the local minimum values of $g$ occur?

List all values of $x$ in increasing order. If an answer field is unused, type an upper-case "N" in it.

Smallest local minimum value at $x =$

Next smallest local minimum value at $x =$

Next smallest local minimum value at $x =$

(c) Where does $g$ attain its absolute maximum value?

$x =$

(d) On what intervals is $g$ concave downward? Give the endpoints of each interval to within the nearest 1/2.

List all $x$-intervals in increasing order. If an answer field is unused, type an upper-case "N" in it.

First interval: (, )

Second interval: (, )

Third interval: (, )

Graph of $f$:

You can earn partial credit on this problem.