Find the indicated derivative

[mikeb]

im having problems with this:

Find F'(2) given that f(2)= -1 , f'(2)= 4, g(2)= 1, and g'(2)= -5

a) F(x)= 5f(x) +2g(x)

 

[tkhunny]

Find F'(2) given that f(2)= -1 , f'(2)= 4, g(2)= 1, and g'(2)= -5

a) F(x)= 5f(x) +2g(x)

I'm having a sneaking suspicion that we are missing part of this problem. There is a bit too much information in the problem statement.

F'(x) = 5*f'(x) + 2*g'(x)
F'(2) = 5*f'(2) + 2*g'(2) = 5*(4) + 2*(-5) -- Too easy.

F(x)= 5[f(x)]² +2[g(x)]² would have been more interesting.

 

[Gene]

Now if it weren't for the typo :twisted:
F'(2) = 5*f'(2) + 2*g'(2) = 5*(4) + 3*(-5)
should read
F'(2) = 5*f'(2) + 2*g'(2) = 5*(4) + 2*(-5)
of course
-----------------
Gene

 

[tkhunny]

Right. Repaired above. Thanks for the heads-up.

Too bad that doesn't clear up my suspicion.

 

[slider2990]

The extra information is what makes these types of problems "tricky" The nature of the problem is to make you think you need to use all the information when you don't. So don't waste any sleep over this problem because you're already right.

 

[tkhunny]

Granted. But I'm still suspicious.

 

[Matt]

It's a multi-part problem. Possibly f(2) and g(2) are used in parts (b), (c), etc.

 

[mikeb]

thanks, i now see that i dont need to use all the given information at once.