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Product Rule (Thinking/Inquiry)

  1. Sep 27, 2008 #1
    Determine a quadratic funtion [tex]f(x) = ax^2 + bx + c[/tex] who graph passes through the point (2,19) and that has a horizontal tangent at (-1,-8).

    My attempt at this solution is:
    [tex]f(x) = ax^2 + bx + c[/tex]
    [tex]f'(x) = 2ax + b[/tex]

    LOL its not much but i really have absolutely no idea where to go from here :S
     
  2. jcsd
  3. Sep 27, 2008 #2

    gabbagabbahey

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    Have you tried substituting the given point and tangent point into the equations for f and f' respectively? What do you get if you do that?
     
  4. Sep 27, 2008 #3
    All i know is
    [tex]f(x) = ax^2 + bx + c[/tex]
    [tex]f'(x) = 2ax + b[/tex]
    [tex]f'(-1) = 2a(-1) + b[/tex]
    [tex]f'(-1) = -2a + b[/tex]
    [tex]0 = -2a + b[/tex] @ x = -1
    [tex]0 = 4a + b[/tex] @ x = 2

    After that i know i have to find 2 variables (a and b) and then finally find c but before i can do that i have to know what to do with those 2 equations which i dont @_@
     
  5. Sep 27, 2008 #4

    gabbagabbahey

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    If f(x) passes through (2,19) then f(2)=19 , similarly if f has a horizontal tangent at (-1,-8), then f'(-1)=0 and f(-1)=8....this should give you 3 equations and 3 unknowns a,b,c which you can solve for. Can you take it from there?
     
  6. Sep 27, 2008 #5
    so u are saying:
    [tex]19=4a+2b+c[/tex] for f(2)=19
    [tex]0=-2a+b[/tex] for f'(-1)=0
    [tex]-8=a-b+c[/tex] for f(-1)=8

    That also means im solving a system of 3 equations correct ? oh crap... i need to review my basics T_T
     
  7. Sep 27, 2008 #6

    gabbagabbahey

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    Yes, but do you understand why f(2)=19, f'(-1)=0 and f(-1)=-8? And yes, you will need to solve a system of 3 equations to determine a b and c.
     
  8. Sep 27, 2008 #7
    YAY !! SOLVED IT

    I DONT NEED HELP ANYMORE it was so simple............... 3 unknowns 3 equations lol sorry for caps this is so exiciting !!
     
  9. Sep 27, 2008 #8
    and yes i do know why ..... i think if u would so kindly tell me i can verify my thought. Is it because we *neeed* 3 equations and the only ones we know are from those 2 co-ordinates
     
  10. Sep 28, 2008 #9

    HallsofIvy

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    No, those are not true because you need them.

    f(2)=19 is true because you were TOLD that the graph goes through (2, 19).
    f'(-1)=0 is true because you were TOLD that the graph has a horizontal tangent at (-1, -8) and a "horizontal tangent" has slope 0.
    f(-1)= -8 because in order to have a tangent line at all at (-1, -8), the graph must include the point (-1, -8).

    The fact that you need three equations to determine the three coeffiencents is why you use them, not why they are true!
     
  11. Sep 28, 2008 #10
    Oh i know that.... i had the grand unification theory in my head. I thought it would be explained in a sentence or so. my bad T_T
     
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