Question

What is the second derivative of `f(x)= 3x^(2/3)-x^2`?

Answer 1

`f''(x) = -2(1/(3x^(4/3))+1)`

Explanation:

`f(x) = 3x^(2/3)-x^2`

`f'(x) = 3* 2/3x^(2/3-1) - 2x` [Power rule]

`= 2x^(-1/3) - 2x`

`f''(x) = 2* -1/3x^(-1/3-1) -2` [Power rule]

`= -2(1/3x^(-4/3)+1)`

`= -2(1/(3x^(4/3))+1)`