Commit 2022-07-17 04:14 d857ca65

feat(analysis/calculus/mean_value): remove assumption in strict_mono_on.strict_convex_on_of_deriv (#15133) Currently, the lemma strict_mono_on.strict_convex_on_of_deriv states that, if a real function f is continuous on a convex set D, differentiable on its interior, and deriv f is strictly monotone on its interior, then f is convex on D. We remove the differentiability assumption: since deriv f is strictly monotone, there is at most one point of nondifferentiability (as deriv f x = 0 when f is not differentiable), and the result is still true (although the proof is a little bit more complicated) in this case. Of course, in essentially all applications the functions will be differentiable, but the lemma becomes easier to use as the user doesn't need to prove this differentiability.