Question: 4. [Maximum mark: 15] A function f has its derivative given by f' (x) = 3x2 - 2kx - 9, where k is a constant.

4. [Maximum mark: 15] A function f has its derivative given by f' (x) = 3x2 - 2kx - 9, where k is a constant. (a) Find f"(x). [2] (b) The graph of f has a point of inflexion when x = 1, Show that k = 3, [4] (c) Find f '(-2). [2] (d) Find the equation of the tangent to the curve of f at (-2, 1), giving your answer in the form y = ax + b. [4] (e) Given that f '(-1) = 0, explain why the graph of f has a local maximum when x = =1, [3]

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