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Homework Help: Tricky difference quotient problem i am stuck

  1. Sep 4, 2010 #1
    1. The problem statement, all variables and given/known data
    find f(a+h)-f(a)/h for the f (x)= 2x+3x2


    2. Relevant equations

    f(a+h)-f(a)/h

    3. The attempt at a solution
    f(a+h)-f(a)/h
    =2(a+h)-3(a+h)2-2x+3x2
    =2a+2h-3a2-3h2-2a+3a2
    =2h-3h2/h

    that is where i am stuck
    help please
     
  2. jcsd
  3. Sep 4, 2010 #2
    First, what is [tex](a + h)^{2}[/tex] ?

    And what is [tex]-f(a)[/tex] equivalent to?
     
  4. Sep 4, 2010 #3
    whoops, (a+h)^2 = a^2+2ah+h^2
    but -f(a) is correct right?
     
  5. Sep 4, 2010 #4
    notice the second line you wrote ([tex]2(a+h)-3(a+h)^{2}-2x+3x^{2}[/tex])

    See something wrong with the last term ?
     
  6. Sep 4, 2010 #5

    Mark44

    Staff: Mentor

    You need more parentheses here.
    This should be (f(a + h) - f(a))/h
    What happened to the h divisor? And as above, the entire numerator needs parentheses around it.
    Still missing the h.
     
  7. Sep 4, 2010 #6
    so 2a+2h-3a^2-6ah-6h^2-2a+3a^2
    =2h-6ah-6h^2/h
    =2h(3a+3)/h
    then what

    oh ok i see
     
  8. Sep 4, 2010 #7
    No, this is still not correct - you are doing your algebra wrong

    [tex]f(a + h) - f(a) =[/tex]
    [tex]f(a + h) - (2x + 3x^{2}) =[/tex]
    [tex]f(a + h) + (-1)*(2x + 3x^{2})[/tex]

    You are not distributing the minus sign correctly

    can you see how to fix it?
     
  9. Sep 4, 2010 #8
    yes, sorry my eyes are not working,
    so i got it down to 2h+6ah+3h^2/h
    so the answer has to be 6a+3h+2
    if not don't bother i quit
     
  10. Sep 4, 2010 #9

    Mentallic

    User Avatar
    Homework Helper

    And the limit is h approaches 0 so you cancel out the h. You can always check your answer by just taking the derivative of the function.
     
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