The function does have a maximum, and we may calculate the derivative as follows:
You are correct that the derivative changes sign at , and as the function decreases after , a maximum occurs here.
does the function y= (x-1)/x^2 have a maximum or a minimum because when i conduct a derivative test there signs change from positive to negative at x=2, but when i graph the function on a graphing calculator there doesn't seem to be a maximum