Question

What is the second derivative of #f(x)=3x^3-18x^2+6x-2 #?

Answer 1

`f''(x)=18x-36=18(x-2)`

Explanation:

First, you have to obtain the first derivate:

`f'(x)=3*3x^(3-1)-18*2*x^(2-1)+6x^(1-1)+0=`
`=9x^2-36x+6x^0=9x^2-36x+6`

Now you derivate again in `x`

`f''(x)=9*2x^(2-1)-36*1x^(1-1)+0=18x-36x^0=`

`=18x-36*1=18x-36=18(x-2)`