Graph of $f^{\text{'}}$

$4.$ Let $f$ be a function defined on the closed interval $-3x4$ with $f(0)=3.$ The graph of $f^{\text{'}},$ the derivative of $f,$ consists of one line segment and a semicircle, as shown above.

$($a$)$ On what intervals, if any, is $f$ increasing? Justify your answer.

$($b$)$ Find the $x-$coordinate of each point of inflection of the graph of $f$ on the open interval $f(0,3)f(-3)f(4)-3.$ Justify your answer.

$(c)$ Find $an$ equation for the line tangent $to$ the graph $offat$ the point $(0,3).$

$(d)$ Find $f(-3)$ and $f(4).$ Show the work that leads $to$ your answers.Graph of $f^{\text{'}}$

$4.$ Let $f$ be a function defined on the closed interval $-3x4$ with $f(0)=3.$ The graph of $f^{\text{'}},$ the derivative of $f,$ consists of one line segment and a semicircle, as shown above.

$($a$)$ On what intervals, if any, is $f$ increasing? Justify your answer.

$($b$)$ Find the $x-$coordinate of each point of inflection of the graph of $f$ on the open interval $f(0,3)f(-3)f(4)-3.$ Justify your answer.

$(c)$ Find $an$ equation for the line tangent $to$ the graph $offat$ the point $(0,3).$

$(d)$ Find $f(-3)$ and $f(4).$ Show the work that leads $to$ your answers.