"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.