This is from MIT OCW single variable calculus, in a section about learning to sketch curves. The material explains that if f'(x) is negative then f(x) is decreasing - this makes sense to me geometrically, if the slope of the tangent is negative then the graph is obviously decreasing.
Now for the question:
Sketch the graph of y = x/(x+4); find the intervals on which it is increasing and decreasing and decide how many solutions there are to y = 0."
And the solution:
y = x/(x+4), y' = 4/(x+4)^2
Increasing on: -4 < x < infinity
Decreasing on: -infinity < x < -4
I can see that the solution is correct, but as far as I can tell, y' > 0 for all values of x (except x = -4).
Is there something I'm missing, algebraically? Or am I just supposed to look at the graph and infer that this is some special case of y'?