Question
Asked Nov 18, 2019
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1. Let f(x) cos2(x) - 2 sin(x) for 0
27
x
(a) Compute f'(x) and use it to find intervals where f(x) is increasing or decreasing for x in
[0, 2m
(b) Find the local extrema of f(x) for x in [0, 27]. Explain
(c) Compute f"(x) and use it to find the intervals of concavity and inflection points of f(x)
for in [0, 27
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1. Let f(x) cos2(x) - 2 sin(x) for 0 27 x (a) Compute f'(x) and use it to find intervals where f(x) is increasing or decreasing for x in [0, 2m (b) Find the local extrema of f(x) for x in [0, 27]. Explain (c) Compute f"(x) and use it to find the intervals of concavity and inflection points of f(x) for in [0, 27

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Expert Answer

Step 1

First compute f'(x) using first derivative. 

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f(x) cos (x)-2sin(x) f'(x) 2cos(x)-sin(x)]-2cos(x) f'(x)-2cos(x)sin(x)+1]|

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Step 2

Then find critical points using f'(x)=0. 

Critical points are= pi/2 and 3pi/2

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f'(x) 0 -2cos(x)[sin(x)+1]=0 sin(x)+1-0 sin(x)- -2cos(x) 0 cos(x) 0 Зл л Зл x=. 2 2 2

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Step 3

Check sign of f\'(x) in each intervals. 

f\'(pi/4) = negative 

f\'(pi)=positive

f\'(7pi/4)= negative 

So, in (0,pi/2) and (3pi/2 , 2pi) the function is decreasing. [because f\...

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3T 2TT 4 FlN

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