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

Explanation

`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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