Maximum and minimum of f(x)=2 \sin^2 x+2 \cos^4 x

Lucille Davidson 2022-01-16 Answered
Maximum and minimum of f(x)=2sin2x+2cos4x
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Bertha Jordan
Answered 2022-01-17 Author has 37 answers
You also could linearise the function first, doing some trigonometry:
2sin2x+2cos4x=1cos2x+122cos2x2=
=1cos2x+12+cos2x+12cos22x
=32+1+cos4x4=7+cos4x4
Now it is obvious this expression has a global minimum when cos4x=1 and a global maximum when cos4x=1
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RizerMix
Answered 2022-01-20 Author has 438 answers
f(x)=2sin2+2(1sin2)cos2x= 2(sin2x+cos2x)2sin2xcos2; f(x)=2(12)sin2(2x); Minimum: at 2x=k2π+π2 kZ; fmin(x)=32; Maximum: at 2x=k2π,  kZ; fmax(x)=2
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