Let f be a function defined on the closed interval with f(0)=3. The graph of f', 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 . Justify your answer.
(c) Find an equation for the line tangent to the graph of f at the point (0,3).
(d) Find f(-3) and f(4). Show the work that leads to your answer.
