1. ## Derivative 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...

2. Originally Posted by RU2010

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...
Start by differentiating g(x) (use the product rule), if you are then still having problems ask again.

CB

3. 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....

4. Originally Posted by RU2010
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....
But the question just asks you to compute g'(2). Why do you need f(x)?

Originally Posted by RU2010

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...

5. 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.

6. 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?

7. Originally Posted by Defunkt
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?
Ok, the light bulb just came on! I see the answer now, and it was staring at me the entire time!

Thanks guys.