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Math Help - Differentiation question ... need help!!!

  1. #1
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    Differentiation question ... need help!!!

    A curve has the equation y=root x(k-x) where k is a constant.
    Given that the gradient of the curve is root 2 at the Point P where x=2.

    a. find the value of k.

    b.show that the normal to the curve at P has the equation
    x+root 2y=c where c is an integer to be found.
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  2. #2
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    someone please help!!!!
    i got the solutions k = 2.5/2.0625
    is the right???
    how about part b) ?
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  3. #3
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    I got k\;=\;12+4\sqrt{6}
    How did you get your value ?
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  4. #4
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  5. #5
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    You made a mistake in the differentiation of y
    (u^n)'\;=\;nu'u^{n-1}

    You forgot u'
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  6. #6
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    what's u'???
    i thought the first derivative is defined as:
    dy/dx = n(x^(n-1))
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  7. #7
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    The first derivative of y=x^n is y'=n x^(n-1)

    But the first derivative of y=(u(x))^n is y'=n u'(x) (u(x))^(n-1)

    Here u(x)=kx-x and n=1/2
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