Chapter 6: Q. 43 (page 419)

find the average rate of change of f from $0$ to $\frac{π}{6}$
role="math" localid="1646338076356" $f (x) = \tan (2 x)$
.

Short Answer

Expert verified

the average rate of change of f $f (x) = \tan (2 x)$ from $0$ to $\frac{π}{6}$ is $\frac{6 \sqrt{3}}{π}$

Step by step solution

Step 1. Given data

The given function is

$f (x) = \tan (2 x)$

The given range is $[a, b] = [0, \frac{π}{6}]$

Step 2. average rate of change

The average rate of change f

$\frac{f (b) - f (a)}{b - a} = \frac{\tan (2 b) - \tan (2 a)}{b - a} = \frac{\tan (2 \times \frac{π}{6}) - \tan (2 \times 0)}{\frac{π}{6} - 0} = \frac{\tan \frac{π}{3} - \tan 0}{\frac{π}{6}} = \frac{\sqrt{3} - 0}{\frac{π}{6}} = \frac{6 \sqrt{3}}{π}$

So average rate of change is $\frac{6 \sqrt{3}}{π}$

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 from $0$ to $\frac{π}{6}$
role="math" localid="1646338076356" $f (x) = \tan (2 x)$
.

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

find the average rate of change of f from0 toπ6role="math" localid="1646338076356" f(x)=tan(2x).

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

find the average rate of change of f from $0$ to $\frac{π}{6}$
role="math" localid="1646338076356" $f (x) = \tan (2 x)$
.