Posted by Hannah on Tuesday, June 5, 2012 at 6:27pm.
If dy/dx = (1 + x)/(xy), x>0, and y=4 when x=1, then when x=3, y= what?

Derivatives ~ Calculus  Count Iblis, Tuesday, June 5, 2012 at 6:43pm
y dy = (1+x)/x dx = (1 + 1/x) dx
Integrate both sides 
Derivatives ~ Calculus  Stewart, Tuesday, June 5, 2012 at 7:06pm
After integrating and solving, I got approximately 4.711393061. Does this seem right?

Derivatives ~ Calculus  Count Iblis, Tuesday, June 5, 2012 at 8:49pm
It's 4.711393061, to find out what sign you need, you need to consider the sign of dy/dx. You can see that because y = 4 at x = 1, dy/dx is negative, so at that point y(x) is negative and decreasing. It can't become positive, because that would require there to be a point where dy/dx = 0 between x = 1 and x = 3( assuming y is continuous), but x + 1/x doesn't become zero on that interval.