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Chapter 4: Q.18 (page 247)

Find the average rate of change of f(x)=x2+3x+1from 1 to 2. Use this result to find the equation of the secant line containing(1,f(1)),(2,(f(2))

Short Answer

Expert verified

The average rate of change is 6.

The equation of secant line isy=6x-1

Step by step solution

01

Given information

We are given af(x)=x2+3x+1

02

Find f(1),f(2)

We substitute the values in the function we get

f(x)=x2+3x+1f(1)=1+3+1f(1)=5alsof(2)=22+3(2)+1f(2)=4+6+1f(2)=11

03

Find average rate of change

Rate of change

=f(2)-f(1)2-1=11-52-1=6

04

Now to find the equation of secant line

The equation of line can be given as

y-y1=m(x-x1)

Substitute

m=6(x1,y1)=(1,5)

We get,

y-5=6(x-1)y-5=6x-6y=6x-1

05

Conclusion

The average rate of change is 6.

The equation of secant line isy=6x-1.

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