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

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.

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.