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Thread: Veriyfing that point given is either maximum or minimum

  1. #1
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    Veriyfing that point given is either maximum or minimum

    Use an algebraic strategy to verify that the point given for the function is either a maximum or minimum.

    f(x) = x3 - 3x; (-1,2)

    The answer should be 0 yet i get another answer. This is what i did:[COLOR=rgb(0, 0, 0)]

    [/COLOR] (a+h)-(a)/h=(-1+h)-(-1)/h=(-1+h)^3-(-3(-1))/h

    (-1+h)(-1+h)(-1+h)=(1-h-h+h^2)(-1+h)=-1+3h-3h^2+h^3

    (-1+3h-3h^2+h^3-3/h

    "h's" cancel

    -1+3-3h+h^2-3=h^2-3h-1

    h=0.01,h=-0.01

    (0.01)^2-3(0.01)-1=-1.0299

    (-0.01)^2-3(-0.01)-1=-0.9699

    -1.0299+(-0.9699)/2=-0.9999

    It should = 0 however and the slopes should be negative right side and positive left side I believe proving it is a maximum.
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  2. #2
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    Check the first step.
    It should be

    \frac{( a + h) - a}{h} It becomes

    \frac{[(-1 + h)^3 - 3(-1 +h)] - [ (-1)^3 -3(-1)]}{h}

    Now proceed.
    Last edited by sa-ri-ga-ma; Feb 25th 2011 at 09:58 PM.
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  3. #3
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    Yeh that's what I did. I'm new with latex so I really ment h dividing that whole part not just "a" which gives me the answer that I got
    Last edited by Devi09; Feb 25th 2011 at 10:01 PM. Reason: Scratch that my firefox didn't load the "it becomes part". I'll check again in the morning cause it's 1 am now
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  4. #4
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    Simplify the numerator and see what you get.
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  5. #5
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    Alright so I tried again hopefully correctly but in the end I still didn't get that 0 i'm looking for

    [tex](-1+h)^3-3(-1+h)-[(-1)^3-3(-1)]/h[\MATH]

    [tex]-1+3h-3h+3h^3-[-1+3][\MATH]

    [tex]-1+1-3+3h-3h+3h^3/h[\MATH]

    "h's cancel plus other numbers"

    [tex]3h-3[\MATH]

    [tex]3(0.01)-3 = -2.97[\MATH]

    [tex]3(-0.01)-3 = -3.03[\MATH]

    [tex]-2.97+(-3.03)/2 = -3[\MATH]

    This time i get -3 instead of 0 and both "h's" left and right sides are negative instead of being left positive and right negative proving it to be a maximum
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  6. #6
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    Alright after many many tries i managed to get a tangent of 0.0001. Not 0 but really really close so I guess that's good enough and I also got the right side to be negative and left side positive proving its a maximum. The problem was that I made a simple but at the same time major mistake simplifying.
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