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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 41 (page 419)

find the average rate of change of f from $0$ to $\frac{蟺}{6}$
role="math" localid="1646337271984" $f (x) = \tan x$
.

Short Answer

Expert verified

the average rate of change of $f (x) = \tan x$ from $0$ torole="math" localid="1646337601973" $\frac{蟺}{6}$ is $\frac{2 \sqrt{3}}{蟺}$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = \tan x$

The given range isrole="math" localid="1646337698106" $[a, b] = [0, \frac{蟺}{6}]$

02

Step 2. average rate of change

the average rate of change f

$\frac{f (b) - f (a)}{b - a} = \frac{\tan (b) - \tan (a)}{b - a} = \frac{\tan (\frac{蟺}{6}) - \tan (0)}{\frac{蟺}{6} - 0} = \frac{\frac{1}{\sqrt{3}} - 0}{\frac{蟺}{6}} = \frac{2 \sqrt{3}}{蟺}$

So average rate of change is $\frac{2 \sqrt{3}}{蟺}$

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