Explanation Given : f ( x ) = tan x on [ 0 , 2 π ] Concept Used: f ( x ) is a function that satisfies two condition: 1. f ( x ) is continuous on the closed interval [ a , b ] 2. f ( x ) is differentiable on the open interval ( a , b ) 3. f ( a ) = f ( b ) Then a number c must be lie between a and b, a < c < b f ' ( c ) = 0 The given function, f ( x ) = tan x on [ 0 , 2 π ] For Rolle’s theorem satisfy the function f ( x ) if 1

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.2, Problem 22PS

To determine

To decide: The number c between the interval [0,2π] which satisfy Roll’s theorem of function f(x)=tanx

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Chapter 4.2, Problem 21PS

Chapter 4.2, Problem 23PS

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Chapter 4 Solutions

Calculus

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To decide: The number c between the interval [ 0 , 2 π ] which satisfy Roll’s theorem of function f ( x ) = tan x

Solution Summary: The author explains that the number c must be lie between a and b to satisfy Roll’s theorem.

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To decide: The number c between the interval [0,2π] which satisfy Roll’s theorem of function f(x)=tanx

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Chapter 4 Solutions