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.

Answer 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