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).
c. does w(x) have an absolute minimum on (-∞,∞)? if so, give the (x,y) coordinates for each occurrence of this minimum.
d. does w(x) have an absolute maximum on (-∞,∞)? if so, give the (x,y) coordinates for each occurrence of this maximum.
e. find the (x,y) coordinates of the absolute maximum(s) of (x,y) on -1,1.
f. find the (x,y) coordinates of the absolute minimum(s) of (x,y) on -1,1.

Explanation:

Step1: Recall local - minimum definition

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

Step2: Identify local minima from the graph

From the graph of \(y = w(x)\), we look for the points where the curve bottoms - out.

Answer:

A. The local minimum occurs at approximately \((2,-3)\)

Step3: Recall local - maximum definition

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

Step4: Identify local maxima from the graph

From the graph, we look for the points where the curve peaks.