Check NEAR the four critical values of x, to the left and to the right of each critical value. The critical values are -2, -1, 1, and 4.
I can only imagine using derivative of y to help find the minimum or maximum value(s). Quotient Rule using y in its non-factored form. The easier way is to use a graphing calculator and find the numeric values for any max or min.
I used the easy way, entering the equation into www.google.com.
Range is all real numbers. No maximum and no minimum.