Question: The first derivative of a certain function is f'(x) = x(x 1) 2 . a. On what intervals is f increasing? Decreasing? b. On

The first derivative of a certain function is f'(x) = x(x − 1)2.

a. On what intervals is f increasing? Decreasing?

b. On what intervals is the graph of f concave up? Concave down?

c. Find the x coordinates of the relative extrema and inflection points of f.

d. Sketch a possible graph of f(x).

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