1. The problem statement, all variables and given/known data Find extrema and points of inflection (then graph it). f(x) = x2e-x 2. Relevant equations 3. The attempt at a solution So, for f'(x) = xe-x(2-x) Critical point(s): f'(x) = 0 2-x = 0 x= 2 I have a question before continuing. Will my critical point include 0 besides 2? I still have doubts about whether 0 is always part of the critical points because my prof., when working on a similar problem, stated that only the number found was the critical point and didn't use zero. He said that e-x cannot be equal to zero. Meaning he used 2 to find the extrema. What he did was using test numbers between 2 to see where it was increasing and decreasing (THAT if I didn't miss any step while copying it - I tend to rush a little when copying the notes on the board since he writes a lot). However, with this problem, my book seems to use 0 as the other point to find extrema. For instance, when substituting 2 and 0 back into the original function, I'll have (2, 4e-2) and (0,0). Being the first , the MAX and the last, the MIN extrema. Does that mean that 0 was the other critical point? Meaning, will 0 ALWAYS be part of the critical point and be used to find the MIN/MAX extrema?