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Chapter 2: Q. 8 (page 126)

For the function f(x)=3x2-2x+4, find the average rate

of change of f from 3to 4.

Short Answer

Expert verified

The average rate of change off(x)=3x2-2x+4form3to4is19

Step by step solution

01

Step 1. Given data

The given function is

f(x)=3x2-2x+4

02

Step 2. The average rate of change 

The average rate of change function is

鈭�y鈭�x=f(b)-f(a)b-a鈭�y鈭�x=3b2-2b+4-(3a2-2a+4)b-a鈭�y鈭�x=3(b2-a2)-2(b-a)b-a鈭�y鈭�x=3(b-a)(b+a)-2(b-a)b-a鈭�y鈭�x=3(b+a)-2

03

Step 3. substitute values

substitute 3 for aand 4 for bin the average rate of change of function

鈭�y鈭�x=3(a+b)-2鈭�y鈭�x=3(3+4)-2鈭�y鈭�x=3(7)-2鈭�y鈭�x=21-2鈭�y鈭�x=19

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Most popular questions from this chapter

Suppose that the x-intercepts of the graph of y=f(x)are-5and 3.

(a) What are the x-intercepts of the graph of y=f(x+2)?

(b) What are the x-intercepts of the graph of y=f(x-2)?

(c) What are thex-intercepts of the graph of y=4f(x)?

(d) What are thex-intercepts of the graph of y=f(-x)?

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

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.

h(x)=12x

If f(x)=x3if-2鈮�x<13x+2if1鈮�x鈮�4

Find: (a)f(-1) (b)f(0) (c)f(1) (d)f(3)

If f(x)=x+1and g(x)=x3, then____________ =x3-(x+1).
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