Question: Let f(x) = x2 + cos(kx), for k > 0.
(a) Graph f for k = 0.5, 1, 3, 5. Find the smallest number k at which you see points of inflection in the graph of f.
(b) Explain why the graph of f has no points of inflection if k ≤ √2, and infinitely many points of inflection if k > .
(c) Explain why f has only a finite number of critical points, no matter what the value of k.