# Derivatives question

1. Oct 3, 2009

### Slimsta

1. The problem statement, all variables and given/known data
If f'(3)=4 and g'(3)=5 then the graph of f(x)+g(x) has slope 9 at x=3.

2. Relevant equations
d/dx f(x)+-g(x) = f'(x)+-g'(x)

lim [f(x+h) + g(x+h)] - [f(x)+g(x)] / h
h>0

3. The attempt at a solution
lim [f(x+h) + cf(x+h)] - [f(x)+cf(x)] / h
h>0

=> lim [f(3+h) + cf(3+h)] - [f(3)+cf(3)] / h
h>0

now what do i do from here?
how can i check if f'(3)=4 and g'(3)=5 is correct?

2. Oct 3, 2009

### aPhilosopher

As stated, just plug what you have into the first of the related equations and simplify. Then it reduces to the definition of the derivative as the slope of the graph of f + g

3. Oct 3, 2009

### Slimsta

yeah but does
lim [f(3+h) + cf(3+h)] - [f(3)+cf(3)] / h
h>0
equal to:
lim 3+h + c3+ch - 3+c3 / h
h>0

?

4. Oct 3, 2009

### aPhilosopher

[[f(3 + h) + cf(3 + h)] - [f(3) + cf(3)]]/h =(1+c)[f(3 + h) - f(3)]/h

then

lim (1+c)[f(3 + h) - f(3)]/h = (1+c) lim [f(3 + h) - f(3)]/h
= (1 + c) f'(3) = (1 + c)4

where every limit in sight is as h goes to 0.

I'm not sure how you were getting what you posted.

5. Oct 4, 2009

### Slimsta

how did you get this part:
(1 + c) f'(3) = (1 + c)4 ?

did you plug in 1+c (c=3) ? or what did you do to find the 4?
now, how do i check if g'(3)=5?

6. Oct 4, 2009

### aPhilosopher

If f'(3)=4 and g'(3)=5 then the graph of f(x)+g(x) has slope 9 at x=3.

You have it as an assumption that f'(3) = 4 and g'(3) = 5 ;)

What exactly are you trying to do with your limit argument?