Question: The graph of the function f(x) = x(1-x) is shown below. The derivative (slope function) of f is found to be f'(x)=-3x(1-x)+(1-x) (Not difficult,

The graph of the function f(x) = x(1-x) is shown below. The derivative (slope function) of f is found to be f'(x)=-3x(1-x)+(1-x) (Not difficult, once we have the rules!) A (a) Factor f'(x), and find all values of x where the tangent to the graph is horizontal, i.e. f'(x) = 0. (b) Determine the exact maximum value of f(x).

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