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Math Help - Differentiation

  1. #1
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    Differentiation

    Help with this question please:
    Find the values of t when the function defined by x = 5t^3 + 2 and y = 3t^2 -5t is concave down.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Refer this site: Sign of 2nd derivative, Maths First, Institute of Fundamental Sciences, Massey University

    Concave down = Slopes decreasing

    \frac{dx}{dt}=15t^2

    \frac{d^2x}{dt^2}=30t

    \frac{dy}{dt}=6t-5

    \frac{d^2y}{dt^2}=6

    \frac{d^2y}{dx^2}=\frac{6}{30t}

    Since the slopes are decreasing,

    \frac{d^2y}{dx^2}<0

    \frac{6}{30t}<0

    t<0
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  3. #3
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    Thanks, I kinda understand what the questions asking but I don't think I'd be able to answer it in a test lol, didn't realise it was an excellence question, nvm. :]
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