prove that - 4 is less than or equal to cos 2 X + 3 sin x is less than or equal to 17 / 8 for all real x
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If you know derivatives then this question can be solved pretty easily.
Differentiate the y = cos2x + 3sinx function with respect to x. Then by dy/dx=0 you'll get some values of x.
Differentiate again to get d²y/dx². Substitute values of x (which you had obtained by dy/dx=0) in this function of d²y/dx².
For d²y/dx² < 0 you'll get maximum value of function. For d²y/dx² > 0 you'll get minimum value of function.
Godspeed!
Differentiate the y = cos2x + 3sinx function with respect to x. Then by dy/dx=0 you'll get some values of x.
Differentiate again to get d²y/dx². Substitute values of x (which you had obtained by dy/dx=0) in this function of d²y/dx².
For d²y/dx² < 0 you'll get maximum value of function. For d²y/dx² > 0 you'll get minimum value of function.
Godspeed!
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