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Math Help - maximum point

  1. #1
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    maximum point

    Find the coordinates of the maximum point on the curve y = -2xsquared + 6x + 3. Explain how you know it is a maximum?

    f'(x) = -4 x + 6
    so maximum point is when f'(x) = 0 so
    -4x + 6 = 0
    -4 x = -6
    x = 1.5

    Sustituing we get

    y = 7.5

    so (1.5, 7.5) is this correct?

    How can I garanty it being the maximum point though?
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    so (1.5, 7.5) is this correct?
    Yes.
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  3. #3
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    Please explain how you know it is a maximum?


    Moderator edit: Added "Please" and deleted excessive ?'s.
    Last edited by mr fantastic; October 28th 2010 at 05:51 PM.
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  4. #4
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    Quote Originally Posted by Natasha1 View Post
    Explain how you know it is a maximum????
    Say the function f(x) has a stationary point at \xi. Then the second derivative test states that \xi is a
    maximum if f''(\xi)<0, and a minimum if f''(\xi)>0, and a possible point of inflexion if f''(\xi) = 0.
    You have f'(x) = -4 x + 6, thus f''(x) = -4. If x = 7.5, we still have f''(x) = -4 <0.
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  5. #5
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    so the second derivative of f'(x) = -4 x + 6 would be

    f''(x) = -4 which is < 0 and hence it is by definition the maximum point
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  6. #6
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    Quote Originally Posted by Natasha1 View Post
    so the second derivative of f'(x) = -4 x + 6 would be

    f''(x) = -4 which is < 0 and hence it is by definition the maximum point
    That's right.
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