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Math Help - Derivatives question

  1. #1
    Member Mr Rayon's Avatar
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    Derivatives question

    Given that y=\frac{x^3}{3}-x^2+x , find \frac{dy}{dx}. Hence show that \frac{dy}{dx}\geq 0 for all x.

    Please show complete working out. Any help will be appreciated.
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  2. #2
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    Quote Originally Posted by Mr Rayon View Post
    Given that y=\frac{x^3}{3}-x^2+x , find \frac{dy}{dx}. Hence show that \frac{dy}{dx}\geq 0 for all x.

    Please show complete working out. Any help will be appreciated.
    y=\frac{x^3}{3}-x^2+x

     y' = x^2 - 2x + 1

    This can be factorised:
     x^2 - 2x + 1 = (x-1)^2

    Since y' is a square number, it has to be zero or positive for all x.
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