To find the min/max of a parabola, we solve with regards to x. Then, for those values of x we find . Say . If then is a minimum point. If , then is a maximum point.
Let . Find the zeroes of and find its min/max points.
First we'll find the zeroes. Solve :
Now we'll find the min/max points. First we find :
So is a critical point. Find :
So is a minimum point, since