In the questions below, if I ask you to give an example of a function, you need to provide a formula for the function. The formula may be piecewise defined.

8. Explain what's wrong with the following solution, and provide a correct solution to the question.

Question. Find the x values for the global maximum and minimum of f (x) = 2x3 3x2 on the interval [1, 2]. Solution. Setting f (x) = 6x2 6x = 0, we get x = 0, x = 1. We apply the second deriviative test. f (x) = 12x 6. Thus f (0) = 6 < 0, f (1) = 6 > 0. Thus the global maximum is attained at x = 0, and the global minimum is attained at x = 1.