
Upper and lower limits
In my homework i have the problem 3x^22x+2 p=[0,1,2,3,4], and i need to solve it by using the definition of the derivative using upper and lower limits. What i am not sure about is how to do the limits when the right side is not always max or min (on 0,1 left side is max but for 1,2 2,3 and 3,4 the right side is max)

Well i made some progress but I'm not sure where I am messing up, I found out I can split the function into two monotonic pieces at x=.75, and I did the left side of it doing a lower limit and it checked out, but the left side I am getting about 10 less then I should, could someone just go through the steps of doing the lower limit so I can see where my error is.