CPM Homework Help : CALC Problem 5-168

The formula $h(x) = (x − 2)(ax − 1)^2$ defines a family of functions, each corresponding to a different value of the parameter, a. Find the values of $x$ for which each of these functions has a relative maximum or minimum; the answers will be in terms of a.

Step 1:

Notice that $h(x)$ is a cubic function. Visualize its graph.
Consequently, it is the location of a local max or min of $h(x)$ .

Step 2:

Since $h(x)$ is a cubic function, there should be another local max or min. Find its location by setting $h^\prime(x) = 0$ and solving for $x$ .

Step 3:

Recall that maxima and minima are $y$ -values. So evaluate $h(x)$ to find the corresponding $y$ -values.