The curve C with equation y = f(x) passes through the point (5, 65). Given that f(x)

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The curve C with equation y = f(x) passes through the point (5, 65). Given that f′(x) = 6x2 − 10x − 12,

a. Use integration to find f(x)

b. Hence show that f(x) = x(2x + 3)(x − 4)

c. Sketch C, showing the coordinates of the points where C crosses the x-axis.

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