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Homework Help: Differentiation help ,

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data

    The curve [tex] y = ax^{2} + bx [/tex] passes through the point (2,4) with gradient 8. Find a and b .

    I have no idea how to work out a and b , do I use simultaneous equations?

    2. Relevant equations



    3. The attempt at a solution

    I have no idea how to work out a and b , do I use simultaneous equations?
     
  2. jcsd
  3. Feb 25, 2009 #2
    well start of by thinking about what your dy/dx would be.....
     
  4. Feb 25, 2009 #3
    okay so dy/dx = [tex] 2ax + b [/tex] from this how do I find what a and b equal ?
     
  5. Feb 26, 2009 #4

    Mark44

    Staff: Mentor

    Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

    Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

    Finally, solve the two equations in a and b simultaneously.
     
  6. Feb 26, 2009 #5
    so I just sub in the values for x and y ?

    are these two equations correct..

    [tex] 4a + b = 4 [/tex]

    [tex] 4a + b = 8 [/tex]

    ?
     
  7. Feb 26, 2009 #6

    danago

    User Avatar
    Gold Member

    Have another look at the first equation.
     
  8. Feb 26, 2009 #7
    x=2 so 2x2=4? can you give more hints, cause I am really stuck

    thank you!
     
  9. Feb 26, 2009 #8
    is it meant to be [tex] 32a + b =4 [/tex] ?
     
  10. Feb 26, 2009 #9

    Mark44

    Staff: Mentor

    No.

    Write your first equation.
    Substitute 2 for x and 4 for y in that equation. The other equation you wrote, 4a + b = 8, is correct.
     
  11. Feb 26, 2009 #10
    [tex] y = ax^{2} + bx [/tex] , [tex] 4a + 2b = 4 [/tex] is this correct? so a = 3 and b = -4 ?
     
  12. Feb 26, 2009 #11

    HallsofIvy

    User Avatar
    Science Advisor

    Check it yourself. IF a= 3 and b= -4, you have y= 3x2- 4x. What is y when x= 2? What is y' when x= 2?
     
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