[Maximum mark: 15] E Let f(:r) = x3 + 3x2 91' + 1:. Part of the graph of f is shown below. The graph of f has a local maximum at A, a. local minimum at B and a point of inection at C. y (a) (i) Find Hm)- (ii) Find f"(a:). (b) Find the az-coordinate of the point of inection at C. Given that f(1) = 14. (c) (i) Find f(0). (ii) Hence. nd the coordinates of the local maximum Mar. 1:) and justify your answer. ((31) Write down in order from least to greatest f\"(B). f'(B}, HR). [4] [2]