Calculus Reposted

A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?

dy/dx=-y/x is my change rate so far, should i substitute the coordinates (x,y) to the equation or just use the decrease rate for x to get the answer?

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  1. the rate at which x changes is given as 2 cm/sec
    which is dx/t.

    so you have to find the derivative with respect to time (t), you found the rate of change of y with respect to x

    xy = 12
    x dy/dt + y dx/dt = 0
    now plug in our given stuff.
    4 dy/dt + 3(2) = 0
    4dy/dt = -6
    dy/dt = -6/4 = -3/2 cm/sec

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