Solving Derivatives Question: Slope 9 at x=3

[Slimsta]

Homework Statement

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

Homework 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

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?

 

[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

 

[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

?

 

[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.

 

[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?

 

[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?