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The difference between the maximum and m...

The difference between the maximum and minimum value of the function `f(x)=3sin^4x-cos^6x` is :

Text Solution

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`f(x) = 3sin^4x-cos^6x`
`= 3sin^4x-(1-sin^2x)^3`
`= 3sin^4x-(1-sin^6x-3sin^2x(1-sin^2x))`
`= 3sin^4x-(1-sin^6x-3sin^2x+3sin^4x)`
`=sin^ 6x + 3sin^2x -1`
`:. f(x) = sin^2x(sin^4x+3) - 1`
Now, `f(x)` will be maximum, when `sinx = 1` and will be minimum when `sin x = 0`.
`:. f(x)_max = 1(1+3)-1 = 3`
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Knowledge Check

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