f(x) = (x + 1)(x 4) 2 a. Sketch the graph of y = f(x). b.

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f(x) = (x + 1)(x − 4)2

a. Sketch the graph of y = f(x).

b. On a separate set of axes, sketch the graph of y = f´(x).

c. Show that f´(x) = (x − 4)(3x − 2).

d. Use the derivative to determine the exact coordinates of the points where the gradient function cuts the coordinate axes.

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