Related Rates Part III

[Hckyplayer8]

How do we determine whether a function is increasing or decreasing at a point?

Test on an interval and if it is greater than 0 it is increasing. Vice versa for decreasing. But we have multiple functions in this problem. So is it as simple as seeing which rate of change is greater?

 

[JeffM]

Test on an interval and if it is greater than 0 it is increasing. Vice versa for decreasing. But we have multiple functions in this problem. So is it as simple as seeing which rate of change is greater?

If the derivative of a function is positive at a point. the function itself is increasing in a neighborhood surrounding that point. If the derivative of a function is negative at a point, the function itself is decreasing in a neighborhood surrounding that point. (There are special nuances if the point is a boundary point.)

One of the two common uses of the derivative is to determine quickly if a function is increasing or decreasing in the neighborhood of a point. This is the very reason I asked you about the sign of the derivative.

 

[lev888]

Test on an interval and if it is greater than 0 it is increasing. Vice versa for decreasing. But we have multiple functions in this problem. So is it as simple as seeing which rate of change is greater?

Test what?
There is one function - the distance between the points.