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.