Question

4.3 max & min on an interval

1. a. find the (x,y) coordinates of all local minimums of w(x).

b. find the (x,y) coordinates of all local maximums of w(x).

Explanation:

Step1: Recall local - minimum definition

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

Step2: Identify from the graph

From the graph of \(y = w(x)\), we look for the low - points in small intervals. We can see that at \(x = 2\), the function \(w(x)\) has a local minimum. The \(y\) - value at \(x = 2\) is \(y=-3\).

Step1: Recall local - maximum definition

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

Step2: Identify from the graph

From the graph of \(y = w(x)\), we look for the high - points in small intervals. We can see that at \(x = 0\), the function \(w(x)\) has a local maximum. The \(y\) - value at \(x = 0\) is \(y = 1\).

Answer:

A. \((2, - 3)\)