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elezavetadrobn
@elezavetadrobn
August 2022
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найдите все значения x, при которых выполняется равенство f'(x) = 0, если f(x)=cos2x + x√3 и x Є [0;п] ?
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sedinalana
Verified answer
F`(x)=-2sin2x+√3=0
sinx=√3/2
x=π/3+2πn U x=2π/3+2πk
0≤π/3+2πn≤π
0≤1+6n≤3
-1≤6n≤2
-1/6≤n≤1/3
n=0⇒x=π/3
0≤2π/3+2πk≤π
0≤2+6k≤3
-2≤6k≤1
-1/3≤k≤1/6
k=0⇒x=2π/3
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Answers & Comments
Verified answer
F`(x)=-2sin2x+√3=0sinx=√3/2
x=π/3+2πn U x=2π/3+2πk
0≤π/3+2πn≤π
0≤1+6n≤3
-1≤6n≤2
-1/6≤n≤1/3
n=0⇒x=π/3
0≤2π/3+2πk≤π
0≤2+6k≤3
-2≤6k≤1
-1/3≤k≤1/6
k=0⇒x=2π/3