Question

Calculus 1 , Help needed to find the monotonicity of a function (Posting function in comments)

Answer 1

The function is (logx-logy)/(x-y) for 0<x<y and 1/y for x=y

Answer 2

So I check if the function is continuous at x=y and it is. Then I check if it is differentiable at x=y and it is, with f'(y)= -1/2y^2

Then I derive the function and get the f'(x) which is attached below

Answer 3

How do I continue from there?