Question

the function h(x) is graphed below. it has domain (-∞, ∞). find all the x - value(s) of the relative maxima of h(x). if there is more than one value, enter the values as a comma - separated list. if there are none, enter none. x = find all the x - value(s) of the relative minima of h(x). if there is more than one value, enter the values as a comma - separated list. if there are none, enter none. x =

Explanation:

Step1: Recall definition of relative maxima

A relative maximum occurs where the function changes from increasing to decreasing.

Step2: Observe the graph

Looking at the graph of \(y = h(x)\), we see it changes from increasing to decreasing at \(x = 1\).

Step3: Recall definition of relative minima

A relative minimum occurs where the function changes from decreasing to increasing.

Step4: Observe the graph for minima

The function changes from decreasing to increasing at \(x=-2\) and \(x = 0\).

Answer:

For relative maxima: \(x = 1\)
For relative minima: \(x=-2,0\)