Max critical point problem (Online calculus course test homework solutions)

Question: When a=175, there is more than one critical point. Considering the x-coordinates of the critical points, what is the value of the greatest x-coordinate, giving your answer to 2 decimal places.



Solution: Critical points are the x values that make the derivative equal to zero. So let's first differentiate f:
Now set it equal to zero and solve for x:



Notice that one solution is when 2x=0, i.e.m x=0 and the other two solutions are given by setting 2x^2-a=0. Let's solve for these x:


Thus, the greatest of these three critical points is +9.35