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Math Help - Help with finding the unkowns

  1. #1
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    Help with finding the unkowns

    Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
    a,b,c,d and e are the unknowns.

    Then 5 equations are:
    f(0)=150
    f(60)=30
    df/dx (60) = 0
    df/dx (180) = 0
    df/dx (300) = 0

    I'm not 100 percent sure on how to approach this. If anyone could give me a kick in the right direction it would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by fetget View Post
    Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
    a,b,c,d and e are the unknowns.

    Then 5 equations are:
    f(0)=150 ... tells you e = 150
    f(60)=30 ... a(60^4) + b(60^3) + c(60^2) + d(60) + 150 = 30
    df/dx (60) = 0 ... 4a(60^3) + 3b(60^2) + 2c(60) + d = 0
    df/dx (180) = 0 ... same drill as above except w/ x = 180
    df/dx (300) = 0 ... ditto w/ x = 300

    solve for a, b, c, and d
    ...
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  3. #3
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    Quote Originally Posted by fetget View Post
    Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
    a,b,c,d and e are the unknowns.

    Then 5 equations are:
    f(0)=150
    f(60)=30
    df/dx (60) = 0
    df/dx (180) = 0
    df/dx (300) = 0

    I'm not 100 percent sure on how to approach this. If anyone could give me a kick in the right direction it would be greatly appreciated.

    f(0)=150 into f(x) = ax^4 + bx^3 + cx^2 + dx + e gives 150 = a(0)^4 + b(0)^3 + c(0)^2 + d(0) + e

    Do you follow? Can you simplify this?
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  4. #4
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    I understand how to get e=150 but I don't know how to work out a,b,c,d.
    Do you have to use simultaneous equations by eliminating the unknowns??
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  5. #5
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    Quote Originally Posted by fetget View Post
    I understand how to get e=150 but I don't know how to work out a,b,c,d.
    Do you have to use simultaneous equations by eliminating the unknowns??
    that's how.
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  6. #6
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    So would I use the 3 differentiated equations to work it out.
    4a(60^3) + 3b(60^2) + 2c(60) + d = 0 Equation (1)
    4a(180^3) + 3b(180^2) + 2c(180) + d = 0 Equation (2)
    4a(300^3) + 3b(300^2) + 2c(300) + d = 0 Equation (3)

    From there I would need to eliminate an unknown.
    Could you help me in getting one of the unknowns for eg. d because I think that one is the easiest.
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  7. #7
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    you forgot an equation ... f(60) = 30

    a(60^4) + b(60^3) + c(60^2) + d(60) + 150 = 30
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  8. #8
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    You need to use 4 equations because you have 4 unknowns
    Last edited by mortalcyrax; April 25th 2010 at 10:08 PM.
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