I was asked to find the minimum and maximum values

Cobie Sadler

Cobie Sadler

Answered question

2022-02-26

I was asked to find the minimum and maximum values ​​of the functions:
1. y=sin2x1+cos2x
2. y=sin2xcos4x

Answer & Explanation

Manraj Horton

Manraj Horton

Beginner2022-02-27Added 6 answers

If you don't really need to use derivatives,
1. Clearly, y=sin2x1+cos2x0 in fact =0 if sinx=0
y1=sin2x1+cos2x1=sin2x(1+cos2x)1+cos2x
=2cos2x1+cos2x0 in fact =0 if cosx=0
y10y10y1
2. y=sin2xcos4x=1cos2xcos4x=1cos2x(1+cos2x)
Now, 0cos2x11cos2x+120cos2x(cos2x+120cos2x(cos2x+1)2
0cos2(cos2x+1)211cos2x(cos2x+1)1

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