5. The graph of a function $f$ consists of a semicircle and two line segments as shown above. Let $g$ be the function given by $g ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$. (a) Find $g ( 3 )$. (b) Find all values of $x$ on the open interval $( - 2,5 )$ at which $g$ has a relative maximum. Justify your answer. (c) Write an equation for the line tangent to the graph of $g$ at $x = 3$. (d) Find the $x$-coordinate of each point of inflection of the graph of $g$ on the open interval $( - 2,5 )$. Justify your answer.
5. The graph of a function $f$ consists of a semicircle and two line segments as shown above. Let $g$ be the function given by $g ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$.\\
(a) Find $g ( 3 )$.\\
(b) Find all values of $x$ on the open interval $( - 2,5 )$ at which $g$ has a relative maximum. Justify your answer.\\
(c) Write an equation for the line tangent to the graph of $g$ at $x = 3$.\\
(d) Find the $x$-coordinate of each point of inflection of the graph of $g$ on the open interval $( - 2,5 )$. Justify your answer.