Derivative Problem.

[RU2010]

Hi, I'm having trouble with a problem. Can anyone help?

Let g(x) = x^3 f(x). Compute g'(2) given that f(2) = 3 and f'(2) = -1.

I have started by differentiating g(x) with the product rule to get g'(x) = 3x^2 f(x) + x^3 f'(x).

Now I'm thinking that the next step would involve finding f(x) since it is part of g(x) so that I could fully differentiate g(x). Given the limited information that f(2) = 3 and f'(2) = -1, how would I solve this problem?

Thanks.

 

[pka]

\(\displaystyle g'(2)=3(2)^2\cdot f(2)+(2)^3\cdot f'(2)\).

 

[BigGlenntheHeavy]

\(\displaystyle given: \ g(x) \ = \ x^3f(x), \ f(2) \ = \ 3 \ and \ f'(2) \ = \ -1, \ find \ g'(2).\)

\(\displaystyle g'(x) \ = \ 3x^2f(x) \ + \ x^3f'(x).\)

\(\displaystyle g'(2) \ = \ ?\)