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.

6. Sketch a graph of a function with a local minimum at x = 1, and a local maxi- mum at x = 3, but f (1) > f (3).

7. Explain what's wrong with the following solution, and provide a correct solution to the question. Question. Find all local minimum and local maximum of the function f (x) = x3 3x. Solution. Setting f (x) = 3x2 3 = 0, we get x = 1. We compute f (1) = (1)3 3 (1) = 2, f (1) = 13 3 1 = 2. Since 2 > 2, we conclude that f (1) is a local maximum, and f (1) is a local minimum.