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Chapter 2: Q. 61 (page 90)

Find the average rate of change of f(x)=-2x2+4

(a) From 0to 2

(b) From 1to 3

(c) From 1to4

Short Answer

Expert verified

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

(b) The average rate of change is-8.

(c) The average rate of change is-10.

Step by step solution

01

Step 1. Given information.

We have:

f(x)=-2x2+4

02

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

The function is f(x)=-2x2+4.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=0,b=2

鈭�y鈭�x=f(2)-f(0)2-0

=-2(22)+4-(-2(0)2+4)2-0=-4

03

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

The function is f(x)=-2x2+4.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=1,b=3

鈭�y鈭�x=f(3)-f(1)3-1鈭�y鈭�x=-2(3)2+4--212+42=-8

04

Part c. Step 1. Find the average rate of change from 1 to 4.

The function is f(x)=-2x2+4.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=1and b=4:

鈭�y鈭�x=f(4)-f(1)4-1鈭�y鈭�x=-2(4)2+4-(-2(1)2+4)3=-10

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