Calculus

An ant is walking along the curve x^2+xy+y^2=19. If the ant is moving to the right at the rate of 3 centimeters/second, how fast is the ant moving up or down when the ant reaches the point (2,3)? Specify direction.

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asked by Anonymous
  1. 2x dx/dt + x dy/dt + y dx/dt + 2y dy/dt = 0
    (dy/dt)(x + 2y) = -2x dx/dt - y dx/dt
    dy/dt(2 + 6) = -4(3) - 3(3)
    dy/dt = -21/8

    the ant is moving DOWN at 21/8 cm/s

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    posted by Reiny

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