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Derivatives question

  1. Oct 3, 2009 #1
    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. jcsd
  3. Oct 3, 2009 #2
    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
     
  4. Oct 3, 2009 #3
    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

    ?
     
  5. Oct 3, 2009 #4
    [[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.
     
  6. Oct 4, 2009 #5
    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?
     
  7. Oct 4, 2009 #6
    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?
     
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