Slope Fields: Understanding & Application

[workerant]

http://www.math.rutgers.edu/~greenfie/webstuff/pdfstuff/w6W.pdf
is the problem

For the first part, I believe it is just tracing, right? I look at the line at (0,1) and then follow it, but it's a little confusing.

Next
It says how many critical points...well a critical point is when it is undefined or has slope zero. It seems like there is a whole line of critical points of slope undefined (i.e. the vertical lines) and a few lines that are horizontal..i.e. slope zero..is that correct or are there not that many? So it would be infinite I believe.

I don't know what they mean by what types? I assume just slope=0 or undefined? I got the relation as y=10/x^2.

 

[lippyka]

Is that right? Yes, you are right. A critical point is a point where the slope of the line is equal to 0 or undefined. There are infinite critical points in this problem since along the vertical lines, the slope is undefined. The relation between x and y is indeed y=10/x^2.