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Chapter 2: Q 46. (page 90)

In Problems 45鈥�52, for each graph of a function y=f(x), find the absolute maximum and the absolute minimum, if they exist.

Short Answer

Expert verified

The absolute maximum is 4and the absolute minimum is0.

Step by step solution

01

Step 1. Given information.

The given graph of the function y=f(x)is:

02

Step 2. Use the concept of absolute maximum and absolute minimum.

Let fdenote a function defined on some interval I. If there is a number uin Ifor which f(x)鈮�f(u)for all xin I, then f(u)is the absolute maximum of fand I.

If there is a number vin Ifor which f(x)鈮�f(v)for all xin I, then f(v)is the absolute minimum of fon I.

03

Step 3. Find the absolute maximum.

The given graph has the closed interval [0,5]as its domain.

We can see from the graph that the given function has maximum value in the interval [0,5]is:

f(4)=4

The largest value of fis f(4)=4.

Therefore, absolute maximum of the function is 4.

04

Step 4. Find the absolute minimum.

We can see from the graph that the given function has two minimum values in the interval [0,5].

f(1)=1f(5)=0

The smallest value of fisf(5)=0.

Therefore, absolute maximum of the function is0.

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