Chapter 4 - Section 4.1 - Maximum and Minimum Values - 4.1 Exercises - Page 283: 14

(a) This is the graph of a function that has two local maxima, one local minimum, and no absolute minimum. (b) This is the graph of a function that has three local minima, two local maxima, and seven critical numbers.

(a) This is the graph of a function that has two local maxima, one local minimum, and no absolute minimum. As the magnitude of $x$ increases in both the negative and positive directions, the graph continues toward the negative values. Therefore, there is no absolute minimum. (b) This is the graph of a function that has three local minima, two local maxima, and seven critical numbers. The two points where the graph is discontinuous are critical numbers, Therefore, the function has seven critical numbers in total.