Find absolute maximum and minimum values of a function `f` given by `f(x)=12 x^(4//3)-6x^(1//3),\ \ x in [-1,\ 1]` .

Explanation

Here, `f(x) = 12x^(4/3) - 6x^(1/3)`

`f'(x) = 16x^(1/3) - 2x^(-2/3) = 16x^(1/3)-2/x^(2/3) = (16x-2)/x^(2/3)`

Now, for maximum and minimum value,

`f'(x) = 0`

`:. (16x-2)/x^(2/3) = 0`

`=>16x - 2 = 0`

`=> x = 1/8`

So, `f(1/8) = 12(1/8)^(4/3)- 6(1/8)^(1/3)`

...