Problem (7) (12 points) Given function y = = f(x) =−x² + 2x + 15. (a) Find f'(x) by the limit definition. (b) Sketch the graph of y = f(x) (include

the z- & y- intercepts and the vertex). (c) Find the equation of the tangent line at x = 2. (d) Find the area of the region enclosed by the curve y = f(x), x=0, x= 1, and the z-axis. [Hint: the graph you have sketched in part (b) may help.]