Increasing Convex Function Increasing Second Derivative? Let $f(x)$ be increasing and convex on a certain interval. Then, $f’’(x)\geq 0$ on this interval. I was wondering if it could be further said that $f’’(x)$ is increasing (or at least non-decreasing) on this interval.
No it can not be said. The second derivative gives you strength of the curvature but since a convex function can have decrasing curvature too the answer is no.
Imagine x^2 beeing cutoff at 1 and then continuoued with constant increase. Then f''(x) = 0 for x &gt;1
No it can not be said. The second derivative gives you strength of the curvature but since a convex function can have decrasing curvature too the answer is no.
Imagine x^2 beeing cutoff at 1 and then continuoued with constant increase. Then f''(x) = 0 for x &gt;1