Example 8 from Algebra and Trigonometry, 3.3 Rates of Change and Behavior of Graphs

Finding Local Extrema from a Graph

Graph the function $f (x) = \frac{2}{x} + \frac{x}{3} .$ Then use the graph to estimate the local extrema of the function and to determine the intervals on which the function is increasing.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Using technology, we find that the graph of the function looks like that in Figure 7. It appears there is a low point, or local minimum, between $x = 2$ and $x = 3,$ and a mirror-image high point, or local maximum, somewhere between $x = −3$ and $x = −2.$

Figure 7

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph the function $f (x) = x^{3} - 6 x^{2} - 15 x + 20$ to estimate the local extrema of the function. Use these to determine the intervals on which the function is increasing and decreasing.

How did it go?

Solution

Your turn

Solution

Your turn