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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:

∆y∆x=f(b)-f(a)b-a

Here, a=2,b=4:

∆y∆x=f(4)-f(2)4-2∆y∆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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Most popular questions from this chapter

In March 2011, Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge -\(13.55

Distribution charge

First 20therms-0.1473/therm

Next 30therm -\)0.0579/therm

Over 50therm -\(0.0519/therm

Gas supply charge-\)0.51/therm

(a) What is the charge for using 40therms in a month?

(b) What is the charge for using 150therms in a month?

(c) Develop a model that gives the monthly charge Cfor x therms of gas.

(d) Graph the function found in part (c).

A right triangle has one vertex on the graph of y=x3,x>0,at x,y, another at the origin, and the third on the positive y-axis at 0,y, as shown in the figure. Express the area Aof the triangle as a function of x.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

g(x)=4x

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2-1

A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=x,ybe the point in quadrant I that is vertex of the rectangle and is on the circle.

Part (a): Express the area A of the rectangle as a function of x.

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph A=Ax. For what value of xis Alargest?

Part (d): Graph p=px. For what value of xis plargest?
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