Commit 2020-12-29 19:06 abffbaa3

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feat(analysis/convex/specific_functions): log is concave (#5508) This PR proves that the real log is concave on Ioi 0 and Iio 0, and adds lemmas about concavity of functions along the way.

Estimated changes

Modified src/analysis/calculus/mean_value.lean

added theorem concave_on_of_deriv2_nonpos

added theorem concave_on_of_deriv_antimono

added theorem concave_on_open_of_deriv2_nonpos

added theorem concave_on_univ_of_deriv2_nonpos

added theorem concave_on_univ_of_deriv_antimono

added theorem convex_on_open_of_deriv2_nonneg

Modified src/analysis/convex/specific_functions.lean

added theorem concave_on_log_Iio

added theorem concave_on_log_Ioi