Solving a Complex Analysis Problem: Finding Critical Points of k(x)

[Treadstone 71]

"Let a,b be in R with a>0 and f(x)=ax^3+bx. Let k(x)=[f''(x)]/[1+(f'(x))^2]^(3/2). Find the critical points of k(x) and use the first derivative test to classify them."

This seems incredibly quantitative and complicated for an analysis assignment. There must be a theorem of some kind I can use to solve this, but I can't see it.

 

[benorin]

I used to think that expressions like "such and such is too complicated for an analysis assignment" just shouldn't be used.

Now that I'm in my second year of analysis courses, I would like my professor to know that expressions like "such and such is too complicated for an analysis assignment" should be employed far more often .