Explanation Let f ( x ) be a continuous function on [a, b] and differentiable in (a, b) then f ( x ) is increasing in [ a , b ] if f ' ( x ) > 0 for each x ∈ ( a , b ) f ( x ) is decreasing in [ a , b ] if f ' ( x ) < 0 for each x ∈ ( a , b ) t ( θ ) = θ + cos θ : 0 ≤ θ ≤ π t ' ( θ ) = 1 − sin θ Let t ' ( θ ) = 0 Critical points will be θ = 1.5707 Now, let’s check the sign of derivative of function. Interval ( 0 , 1.5707 ) ( 1.5707 , 3.14 ) Sign of t ' ( θ ) + + Interval of increasing is ( 0 , 1

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 4.3, Problem 31PS

To determine

The monotonicity, concavity and graph of t(θ)=θ+cosθ:0≤θ≤π

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Chapter 4.3, Problem 30PS

Chapter 4.3, Problem 32PS

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Chapter 4 Solutions

Calculus

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The monotonicity, concavity and graph of t ( θ ) = θ + cos θ : 0 ≤ θ ≤ π

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The monotonicity, concavity and graph of t(θ)=θ+cosθ:0≤θ≤π

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Chapter 4 Solutions