Question

here is a graph of the function h. use the graph to find the following. if there is more than one answer, separate them with commas. all values at which h has a local maximum: all local maximum values of h:

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function occurs at a point where the function value is greater than or equal to the values of the function at nearby points. On a graph, it is a "peak".

Step2: Identify x - values of local maxima

Looking at the graph of \(h(x)\), the x - values at the peaks are \(x=- 1,2\).

Step3: Identify the local - maximum values

The corresponding y - values (function values) at \(x = - 1\) and \(x = 2\) are \(y = 2\).

Answer:

All values at which \(h\) has a local maximum: \(-1,2\)
All local maximum values of \(h\): \(2\)