Question 31: Given a definite and continuous function y = f (x) on \(\mathbb{R}\) and a derivative function f ‘(x) of f(x) with a graph as shown below. Find the maximum number of points of the function.

Look at the graph of the derivative function:

The function f'(x)=0 has 3 solutions and the function f'(x) does not change sign when it passes through those 3 points. So the function y=f(x) has no extremes.

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