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

Lucille Davidson

Lucille Davidson

Answered question


Maximum and minimum of f(x)=2sin2x+2cos4x

Answer & Explanation

Bertha Jordan

Bertha Jordan

Beginner2022-01-17Added 37 answers

You also could linearise the function first, doing some trigonometry:
Now it is obvious this expression has a global minimum when cos4x=1 and a global maximum when cos4x=1


Expert2022-01-20Added 656 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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