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Q. 37

Found in: Page 261


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use a sign chart for f' to determine the intervals on which each function f is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648370582124" f(x)=sinx.cosx

Ans: Increasing interval [-π4+πk,π4+πk]

and decreasing elsewhere.

See the step by step solution

Step by Step Solution

Step 1. Given information:


Step 2. Finding the derivative of the function:

f(x)=sinx.cosxf'(x)=sinx(-sinx)+cosxcosxf'(x)= cos2x-sin2xf'(x)=cos2xlet f'(x)=0 cos2x =02x=2k+1π2 x=2k+1π4 [where k is any integer] taking point x=0

Step 3. Finding increasing and decreasing intervals:

Intervals of the given function :
f'(x) has x=0f'(0)=cos(2.0) =cos0 =1 >0

f(x)is increasing on the interval [-π4+πk,π4+πk]

and decreasing elsewhere.

Step 4. Verifying algebraic answers with graphs :

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