Question
Asked Nov 1, 2019
Find the absolute minimum and absolute maximum values of f on the given interval
2sin2t after differentiating in order to be able to factor the derivative.
Hint: You will need to use the identity cos 2t = 1 -
= 16 cos t + 8 sin 2t,
f(t)
[0, π/2]
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Find the absolute minimum and absolute maximum values of f on the given interval 2sin2t after differentiating in order to be able to factor the derivative. Hint: You will need to use the identity cos 2t = 1 - = 16 cos t + 8 sin 2t, f(t) [0, π/2]

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Step 1

Given function is 

f(t)=16 cost +8 sin 2
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f(t)=16 cost +8 sin 2

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Step 2

To find critical point of f(t) , we solve f'(t)=0

f(t)=-16 sin t +16 cos 2
f(t)0
-16 sint 16 cos2t 0
-sintcos2t 0
sint(12 sin2t)= 0
2 sin2tsint-1= 0
2 sin2t2 sin t - sint-1 0
(2 sint 1(sint+1)= 0
1
sint 1
2
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f(t)=-16 sin t +16 cos 2 f(t)0 -16 sint 16 cos2t 0 -sintcos2t 0 sint(12 sin2t)= 0 2 sin2tsint-1= 0 2 sin2t2 sin t - sint-1 0 (2 sint 1(sint+1)= 0 1 sint 1 2

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Step 3

Since t lies in [0,pi/2], so only critical ...

sint
t=
6
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sint t= 6

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Tagged in

Math

Calculus

Derivative