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.
$f (x) = \frac{1}{s i n x}$

Ans: Increasing interval $[- \frac{π}{4} + πk, \frac{π}{4} + πk]$

and decreasing elsewhere.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information:

$f (x) = \frac{1}{sinx}$

Step 2. Finding the derivative of the function:

$f (x) = \frac{1}{\sin x} = \cos e c x f^{'} (x) = - \cos e c x . c o t x l e t f^{'} (x) = 0 ∴ - \cos e c x . c o t x = 0 \Rightarrow \cos e c x . c o t x = 0 \Rightarrow \frac{1}{\sin x} . \frac{\cos x}{\sin x} = 0 \Rightarrow \frac{\cos x}{\sin^{2} x} = 0 \Rightarrow \cos x = 0 x = (2 k + 1) \frac{π}{2} [w h e r e k i s a n y i n t e g e r] t a k i n g p o i n t x = 0$

Step 3. Finding increasing and decreasing intervals:

Intervals of the given function :

$f^{'} (x) h a s x = 0 f^{'} (0) = \cos (2.0) = \cos 0 = 1 > 0 f^{'} (\frac{π}{2}) = \cos (2 . \frac{π}{2}) = \cos π = - 1 < 0$

f(x)is increasing on the interval $[- \frac{π}{4} + πk, \frac{π}{4} + πk]$

and decreasing elsewhere.

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Calculus

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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.
$f (x) = \frac{1}{s i n x}$

Step by Step Solution

Step 1. Given information:

Step 2. Finding the derivative of the function:

Step 3. Finding increasing and decreasing intervals:

Step 4. Verifying algebraic answers with graphs :

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Step by Step Solution

Step 1. Given information:

Step 2. Finding the derivative of the function:

Step 3. Finding increasing and decreasing intervals:

Step 4. Verifying algebraic answers with graphs :

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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.
$f (x) = \frac{1}{s i n x}$