1. The problem statement, all variables and given/known data So you know the quadratic equations questions like say find the range/ max and min value of the function (x^2-2x+4)/(x^2+2x+4) 2. Relevant equations (x^2-2x+4)/(x^2+2x+4) 3. The attempt at a solution So the typical method for this question is assuming this function to be some y, then forming the quadratic and then finally applying D>0 . However now after a year, at a position where i know basic calculus i can diffn this function to find the critical pts. MY QUESTION TO YOU is this. Will the answer from this shortcut, per say , be always correct and in accordance with the long typical method. Thank you.