Math Problem

Discussion in 'Mac Programming' started by Quboid, Nov 20, 2006.

  1. Quboid macrumors 6502

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    #1
    I know programming is math and logic ( and creativity), and i was just wondering if anybody here could help me derive a caculus question that got me pulling my hair out.
    x(1-x)^2

    thats: x multiplied by 1-x in bracket squared. I am expected to derive this and find the values for x in teh first derivative, i.e, equate it to zero and solve for x.

    thanks guys
     
  2. exabytes18 macrumors 6502

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    #2
    Are you looking for a programming solution or a calculus solution?
     
  3. n-abounds macrumors 6502a

    n-abounds

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    #3
    Wait, is it:

    (x(1-x))^2

    or

    x((1-x)^2))

    ?

    I think either interpretation is quite easy. Just simplify either expression, then use the power rule. Maybe you don't know the power rule... Anyways, after using the power rule you would set that equal to zero and solve for x.
     
  4. nordesmic macrumors member

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    #4
    If I understand you correctly, and I can still remember my chain rule and product rule, the answer would be..

    x*2(1-x)*-1 + 1*(1-x)^2 =0

    that is use the chain rule on the bit with the brackets and then apply the product rule.

    Then the answer would be 2x^2+2x+1-2x+x^2=0
    therefore 3x^2-4x+1=0
    therefore x=.333 or 1

    I hope that is right.
     
  5. n-abounds macrumors 6502a

    n-abounds

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    Mar 6, 2006
    #5
    Hmm I get either:

    1 - 4x + 3x^2 = 0

    or

    2x - 6x^2 + 4x^3 = 0

    depending on how that exponent is interpreted. The answer should be the same whether simplified first, or whether the product and chain rules are used first...

    Nordesmic, you did it right except in the first line where you have "1*2(1-x)*-1 + 1*(1-x)^2 =0" You shouldn't have taken the derivative of x on the left-hand side of the expression...so you should have had "x*2(1-x)*-1 + 1*(1-x)^2 =0" But this mistake throws off the answer you gave...
     
  6. nordesmic macrumors member

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    Adelaide, Australia
    #6
    Yep I fixed it now, should be perfect.
     
  7. Mord macrumors G4

    Mord

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  8. TBi macrumors 68030

    TBi

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    #8
    The exponent always takes precedence over a multiplication.
     
  9. dmcxii macrumors newbie

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    Feb 22, 2006
    #9
    more description.....

    finding derivative of x(1-x)^2

    first get rid of parenthesis
    x(1-x)(1-x)
    multiply it all out
    (x-x^2)(1-x)
    multiply it out again
    x-x^2-x^2+x^3
    combine like terms
    x-2x^2+x^3
    take derivative.....
    1-4x+3x^2
    put in correct form
    3x^2-4x+1
    factor
    (3x-1)(x-1) and solve for zeroes..... x=1, 1/3
     
  10. Eraserhead macrumors G4

    Eraserhead

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    #10
    dmcxii is completely correct

    A solution as an image from Pages+LaTeX (which looks pretty)
    Picture 13.png
     
  11. AJ Muni macrumors 65816

    AJ Muni

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  12. dmcxii macrumors newbie

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    Feb 22, 2006
    #12
    thanks for cleaning it up....

    I knew someone would clean up my typing.

    thanks
     
  13. Quboid thread starter macrumors 6502

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    #13
    Wish it was that easy guys. Thanks for all the help though. I made a mistake with the question. I just got from school and realise that the power that i gave the expression was wrong. It was the square root of everything in the bracket. That would be:
    x(1-x)^1/2.
    taking into consideration that everything raised to the power of one half is the root. Deriving using the chainerule would be perfect, its the simplifing and finding "x" values that got me. Any help??
     
  14. TequilaBoobs macrumors 6502a

    TequilaBoobs

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    Nov 12, 2006
    #14
    youre violating the ethics code at your school - do your own homework.
     
  15. Eraserhead macrumors G4

    Eraserhead

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    #15
    Follow it through in the same way, except replace the 2 with 1/2, should be pretty easy, especially if you follow through my method, think of it as an example ;).
     
  16. Quboid thread starter macrumors 6502

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    #16
    I have alraedy deferenciated it, its just the the simplification and solving for x. You see, when we deferenciate, we would be left with -1/2 as one of the powers, forcing us into a fraction and that's where things get messy.

    This is not homework, its practice for upcomming finals. Its one of the only sums i cant seem to simplyfy, or better yet, i am not sure of my answer.
     
  17. Eraserhead macrumors G4

    Eraserhead

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    #17
    Well try and get one side of the equation (assuming the other side is 0) to only have a single denominator (number on the bottom), but multiplying the top of any other parts by the bottom, then as it equals 0 you can just cancel the denominator away.
     
  18. Quboid thread starter macrumors 6502

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    #18
    thats what i did.And wasn't sure of. thanks alot man.
     
  19. wms121 macrumors regular

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    Mar 1, 2003
    #20
  20. Am3822 macrumors 6502

    Am3822

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    #21
    A question to the OP -- what/where are you studying (hs/college)?

    If this forum is about to become a math questions' forum, maybe someone should install the TeX module :)
     

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