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A particle is moving along the curve y= 3 \sqrt{3 x + 4}. As the particle passes through the point (4, 12), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

  • Calc -

    is the curve
    y = 3/√(3x + 4) ??

    if so, then the particle does not pass through your given point (4,12)

    after you establish where your error is,
    the method to solve the problem would be:

    differentiate your equation with respect to t

    your differential equation contains a dy/dt and a dx/dt term.
    sub in dx/dt = 4 when x = ? and y = ? from the correct given point.

    now the distance from the origin of a general point on the curve is

    d^2 = x^2 + y^2
    2d(dd/dt) = 2x(dx/dt) + 2y(dy/dt)

    sub in all the stuff from above

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