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Find the absolute maximum//minimum value...

Find the absolute maximum`//`minimum value of following functions
`(i) f(x) =x^(3) " "," "x in [-2,2]`
`(ii) f(x) =sin +cosx" "," " x in [0,pi]`
`(iii) f(x) =4x -(x^(2))/(2) " " , " " x in [-2. (9)/(2)]`
`(iv) f(x) =3x^(4) -8x^(3) +12x^(2) -48x+25 " ", " " x in [0,3]`
`(v) f(x) =sin x + (1)/(2) cos 2 x " " , " " x in [0,(pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
(i) max =8, min, =-8
(ii) max `=sqrt(2) ,` min =-1
(ii) max =8 , min =-10
(iv) max =25 , min =-39
(v) max at `x=pi//6` max value `=3//4; ` min at `x=0` and `pi//2` min value `=1//2`
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