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 the definition of local maximum

A local maximum of a function \(y = h(x)\) occurs at a point \(x = a\) if \(h(a)\geq h(x)\) for all \(x\) in some open interval containing \(a\). Visually, it is a "peak" on the graph.

Step2: Identify \(x -\)values (values of \(a\)) for local maxima

Looking at the graph, the \(x -\)coordinates of the peak - points (local maxima) are \(x = 1,x = 3\).

Step3: Identify \(y -\)values (local maximum values)

The \(y -\)coordinate of a point \((x,y)\) on the graph of \(y = h(x)\) gives the value of the function. For \(x = 1\), let the \(y -\)value be \(y_1\) and for \(x = 3\), let the \(y -\)value be \(y_3\). From the graph, the local maximum values (the \(y -\)values of the peak - points) are \(y = 2,y = 2\)

Answer:

All values at which \(h\) has a local maximum: \(1,3\)
All local maximum values of \(h\): \(2,2\)