Consider the differential equation dy/dx = (3-x) / y
Let y= f(x) be the particular solution to the given differential equation for 1 < x < 5 such that the line y = -2 is tangent to the graph of f. Find the x-coordinate of the point of tangency, and determine whether f has a local maximum, minimum, or neither at this point. Justify your answer.
I was able to find the coordinate (x= 3) because the slope is equal to 0 at the point of the tangecy 3-3/y = 0, but I am unsure of how to find whether it is a min/max/neither. It'd be great if someone could help me understand how to do this!
Let y= f(x) be the particular solution to the given differential equation for 1 < x < 5 such that the line y = -2 is tangent to the graph of f. Find the x-coordinate of the point of tangency, and determine whether f has a local maximum, minimum, or neither at this point. Justify your answer.
I was able to find the coordinate (x= 3) because the slope is equal to 0 at the point of the tangecy 3-3/y = 0, but I am unsure of how to find whether it is a min/max/neither. It'd be great if someone could help me understand how to do this!