CPM Homework Help : CALC Problem 5-168

The formula h(x) = (x − 2)(ax − l)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. Homework Help ✎

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 '(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.