? 發問於 科學及數學數學 · 1 十年 前

Differentiation ~*

A point moves in a straight line so that its distance from a fixed point O of that line is 27t - t^3 ,after t sec. Show that it moves aways from O for 3 sec.

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  • 1 十年 前
    最佳解答

    A point moves in a straight line so that its distance from a fixed point O of that line is 27t - t³ ,after t sec. Show that it moves aways from O for 3 sec.

    Let d(t) = 27t - t³

    Change of d(t)

    = d'(t)

    = d(27t - t³)/dt

    = 27 - 3t²

    The shortest distance from point O when the change of d(t) = 0

    i.e. d'(t) = 0

    27 - 3t² = 0

    9 - t² = 0

    t² = 9

    t = 3 or t = -3 (rejected as t ≧ 0)

    So before t = 3, it's moving towards point O.

    After t = 3, it's moving away from O.

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