Chapter 4: Q.18 (page 247)

Find the average rate of change of $f (x) = x^{2} + 3 x + 1$ from 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 is $y = 6 x - 1$

Step by step solution

Given information

We are given a $f (x) = x^{2} + 3 x + 1$

Find f(1),f(2)

We substitute the values in the function we get

$f (x) = x^{2} + 3 x + 1 f (1) = 1 + 3 + 1 f (1) = 5 a l s o f (2) = 2^{2} + 3 (2) + 1 f (2) = 4 + 6 + 1 f (2) = 11$

Find average rate of change

Rate of change

$= \frac{f (2) - f (1)}{2 - 1} = \frac{11 - 5}{2 - 1} = 6$

Now to find the equation of secant line

The equation of line can be given as

$y - y_{1} = m (x - x_{1})$

Substitute

$m = 6 (x_{1}, y_{1}) = (1, 5)$

We get,

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

Conclusion

The average rate of change is $6$ .

The equation of secant line is $y = 6 x - 1$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Given information

Find f(1),f(2)

Find average rate of change

Now to find the equation of secant line

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Mechanics Maths

Decision Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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

Step by step solution

Given information

Find f(1),f(2)

Find average rate of change

Now to find the equation of secant line

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Mechanics Maths

Decision Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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