Answered: Given p(x)= sin2x+sinx on the domain…

Given p(x)= sin2x+sinx on the domain [0,2pi] a) Find the intervals on which p(x) is increasing an dthe intervals in which p(x) is decreasing. b) Find the local maximum and minimum values of p(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 56E

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Question

Given p(x)= sin²x+sinx on the domain [0,2pi]

a) Find the intervals on which p(x) is increasing an dthe intervals in which p(x) is decreasing.

b) Find the local maximum and minimum values of p(x).

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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