### Home > APCALC > Chapter 5 > Lesson 5.5.2 > Problem5-169

5-169.

The formula h(x) = (x – 2)(ax – 1)2 defines a family of functions, each corresponding to a different value of the parameter, a. Determine the values of x for which this family of functions has a relative maximum or minimum. Your answers will be in terms of a. Homework Help ✎

Notice that h(x) is a cubic function. Visualize its graph.

$\text{There will be two roots: }x=2\text{ and }x=\frac{1}{a}.$

$\text{Notice that }x=\frac{1}{a}\text{ is the location of a DOUBLE ROOT;}$

consequently, it is the location of a local max or min of h(x).

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.

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