1. ## 2nd Derivatives

Okay I know how to go about getting a derivative and 2nd derivatives. However, for this problem I can't figure out how to get to the right answer.

this is the function f(x) = x(x-4)^3

2. Originally Posted by sgonzalez90
Okay I know how to go about getting a derivative and 2nd derivatives. this is the function f(x) = x(x-4)^3
The first derivative is $f'(x)=(x-4)^3+3x(x-4)^2$.
You finish.

3. Originally Posted by Plato
The first derivative is $f'(x)=(x-4)^3+3x(x-4)^2$.
You finish.
Yes I got the first derivative already. I wasn't able to get the 2nd.

4. Originally Posted by sgonzalez90
Yes I got the first derivative already. I wasn't able to get the 2nd.
Use a combination of the product rule and the chain rule. Hint:

$(x-4)^3+3x(x-4)^2 = (x-4)^3 + (3x \times (x-4)^2)$

5. You cannot find the derivative of $(x-4)^3+3x(x-4)^2$?
You are joking, right?

6. Originally Posted by Plato
You cannot find the derivative of $(x-4)^3+3x(x-4)^2$?
You are joking, right?
I tried this and got a big mess of a problem but this is what i got

3x-12 (x-4)^2 + (6x^2-24x)^2(x-4)

7. $f'(x)=(x-4)^3+3x(x-4)^2$

$f"(x)=3(x-4)^2+3(x-4)^2+6x(x-4)$

That is it.