Question

In Exercise, find the second derivative of f.
f(x) = x2(x + 1) - 3x3

Answer 1

The second derivative of f is
`f''(x) = -12x + 2`

Explanation:

The derivative of an addition/subtraction of terms is the addition/subtraction of the derivatives of these terms.

The second derivative is the derivative of the first derivative. The third derivative is the derivative of the second derivative. And so goes on...

The derivative of
`a*x^(n)` is
`a*n*x^(n-1)`. The derivative of
`x^(3)` is
`3x^(2)`, for example.

In this problem, we have that:

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

The first derivative is:

`f'(x) = -6x^(2) + 2x`

The second derivative is:

`f''(x) = -12x + 2`