An object moves along the graph of y = f(x). At a certain point, the slope of the curve is 1/2 and the x coordinate of the object is decreasing at the rate of 3 units per second. At that point, how fast is the y-coordinate of the object changing?

This is the problem. What is that 1/2? Isn't it the rate of change of Y, since it is the slope at that point?
How would you solve it?

Question

An object moves along the graph of y = f(x). At a certain point, the slope of the curve is 1/2 and the x coordinate of the object is decreasing at the rate of 3 units per second. At that point, how fast is the y-coordinate of the object changing?

This is the problem. What is that 1/2? Isn't it the rate of change of Y, since it is the slope at that point?
How would you solve it?

anonymous · Answer

The tangent at that particular point has gradient 1/2.  It's the rate of change of y with respect to x, at that particular point.  f'(x)=1/2 at that point.