FREE RESPONSE OUESTION

Let $f$ be the continuous function defined on $-4,3$ whose graph, consisting of three line segments and semicircle centered at the origin, is given at right. Let $g$ be the function given by $g(x)={\displaystyle \underset{1}{\overset{x}{}}}f(t)dt.$

$(2$ points$)$

a$)$ Find the values of $g(2)$ and $g(3).$

b$)$ For each of $g^{\text{'}}(-4)$ and $g^{\text{'}\text{'}}(-3),$ find the value or state that it does not exist.

$(2$ points$)$

Find the $x-$coordinate of each point at which the graph of $g$ has a horizontal tangent line. For each of these points, determine whether $g$ has a relative minimum, relative maximum or neither a minimum or maximum at the point. Justify your answers. $(3$ points$)$

For $xg-4,$ find all values $ofx$ for which the graph $ofg$ has a point $of$ inflection. Explain your reasoning. $(3$ points$)$