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Chapter 2: Q. 62 (page 90)

Find the average rate of change of f(x)=-x3+1

(a) From0to2

(b) From1to3

(c) From-1to1

Short Answer

Expert verified

(a) The average rate of change is -4.

(b) The average rate of change is -13.

(c) The average rate of change is -1.

Step by step solution

01

Step 1. Given information.

We have:

f(x)=-x3+1

02

Part a. Step 1. Find the average rate of change from 0 to 2.

The function is f(x)=-x3+1.

Average rate of change is given by:

localid="1646218831507" 鈭�y鈭�x=f(b)-f(a)b-a

Here, a=0and b=2:

localid="1646217782079" 鈭�y鈭�x=f(2)-f(0)2-0鈭�y鈭�x=-23+1--03+12=-4

03

Part b. Step 1. Find the average rate of change from 1 to 3.

The function is f(x)=-x3+1.

Average rate of change is given by:

localid="1646217897240" 鈭�y鈭�x=f(b)-f(a)b-a

Here, a=1and b=3:

localid="1646217942520" 鈭�y鈭�x=f(3)-f(1)3-1鈭�y鈭�x=-33+1--33+12=-13

04

Part c. Step 1. Find the average rate of change from -1 to 1.

The function is f(x)=-x3+1.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=-1and a=1:

鈭�y鈭�x=f(3)-f(1)-1-1鈭�y鈭�x=-13+1---13+1-2=-1

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Most popular questions from this chapter

A circle of radius ris in inscribed in a square. See the figure.

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f(x)=x2-1
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