HI Dr Sasho,
here is my problem that i couldn't solve.
An ant walks along a cable hanging in the shape of a parabola y= x^2-2x+2, where x and y are in meters. If the x-coordinate of the ant is decreasing at 0.05 m/s when it is at the point (2,2), how fast is its distance from the point (3,0) changing at this point?
thanks for replying,
The distance between (3,0) and any other point (x,y) is Square root of (3-x)2+y2. If the point (x,y) is on the parabola, then y=x2-2x+2, so that the distance function becomes Square root of (3-x)2+(x2-2x+2)2. Now differentiate this function with respect to time and use the given data (that dx/dt=-0.05 and that x=2 at the given moment).