1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    Staff Emeritus
    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook