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Chapter 2: Q. 69 (page 91)

h(x)=x2-2x

(a) Find the average rate of change from 2to 4.

(b) Find the equation of the secant line containing 2,h2and 4,h4.

Short Answer

Expert verified

(a) The average rate of change is 4.

(b) The equation of the secant line isy=4x-8.

Step by step solution

01

Step 1. Given information.

We have:

h(x)=x2-2x

02

Part a. Step 1. Find the average rate of change from 2 to 4.

The function is h(x)=x2-2x.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=2,b=4:

鈭�y鈭�x=f(4)-f(2)4-2鈭�y鈭�x=42-24-22-222=4

03

Part b. Step 1.  Find the equation of the secant line. 

The function is h(x)=x2-2xand the points 2,h2and 4,h4.

Substitute x=2:

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

The slope of the secant line is equal to the average rate of change of a function, it follows:

m=4

Therefore, use the point-slope form to equation of the secant line:

localid="1646233751395" y-y1=msecx-x1y-0=4x-2y=4x-8

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