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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. 80 (page 411)

Find the average rate of change off form $0$ to $\frac{蟺}{2}$ .
role="math" localid="1646562159596" $f (x) = \cos (2 x)$

Short Answer

Expert verified

The average rate of change of $f (x) = \cos (2 x)$ from $0$ to $\frac{蟺}{2}$ islocalid="1646563279500" $0 .$

Step by step solution

01

Step 1. Given data

The given function is

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

The given interval is $(0, \frac{蟺}{2})$

02

Step 2. The average rate of change

differentiate function

$f (x) = \cos (2 x) f' (x) = - 2 \sin (2 x)$

Consider $(a, b) = (0, \frac{蟺}{2})$

The average rate of change

localid="1646563266950" $\frac{f' (b) - f' (a)}{b - a} = \frac{f' (\frac{蟺}{2}) - f' (0)}{\frac{蟺}{2} - 0} = \frac{- 2 \sin (2 (\frac{蟺}{2})) + 2 \sin (2 (0)))}{\frac{蟺}{2} - 0} = = \frac{- 2 \sin (蟺) + 2 \sin (0)}{\frac{蟺}{2}} = \frac{- 0 + 0}{\frac{蟺}{2}} = 0$

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