Can someone please help me solve this problem:

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

Any help with this problem would be much appreciated...

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- Aug 25th 2010, 11:23 PMRU2010Derivative Problem
Can someone please help me solve this problem:

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

Any help with this problem would be much appreciated... - Aug 25th 2010, 11:29 PMCaptainBlack
- Aug 26th 2010, 08:09 PMRU2010
Ok, I have differentiated g(x) = x^3 f(x) , which is g'(x) = 3x^2 f(x) + x^3 f'(x). Given that f(2) = 3 and f'(2) = -1, how do I find out what f(x) is? I'm stuck....

- Aug 26th 2010, 09:13 PMIsomorphism
- Aug 27th 2010, 04:43 AMRU2010
f(x) is part of g(x), so I think I need to know what f(x) is in order to full differentiate g'(x). Since the problem gives the value of f(2)=3, and f'(2), I'm trying to use that information to find f(x). I'm still stuck.

- Aug 27th 2010, 04:53 AMDefunkt
But as they said, you don't need to explicitly find f(x).

The derivative of g(x) is $\displaystyle g'(x) = 3x^2f(x) + x^3f'(x)$

You need to find $\displaystyle g'(2) = 3 \cdot 2^2 \cdot f(2) + 2^3 \cdot f'(2)$. You have f(2) and f'(2) - what more do you need? - Aug 27th 2010, 05:02 AMRU2010