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 Mar19 comment Define the Riemann integral via trapezoids instead of rectangles Yes I am still interested. Mar17 comment Define the Riemann integral via trapezoids instead of rectangles By the "nontrivial direction" I mean the part that integrability in the trapezoidal sense implies Riemann integrability. Mar17 comment Define the Riemann integral via trapezoids instead of rectangles Thanks. Can you give more details for the nontrivial direction of the equivalence? Mar17 revised Define the Riemann integral via trapezoids instead of rectangles edited tags Mar16 comment Define the Riemann integral via trapezoids instead of rectangles Thanks for the idea. How to get it for general functions? Mar16 asked Define the Riemann integral via trapezoids instead of rectangles Feb11 revised Continuity of third derivative in extremum test changed tag Feb10 revised Continuity of third derivative in extremum test edited tags Feb10 comment Continuity of third derivative in extremum test @rubik Just the topological interior of $I$. Feb10 asked Continuity of third derivative in extremum test Jan5 awarded Popular Question Dec15 awarded Caucus Dec15 revised Condition of the mean value theorem edited tags Dec15 comment Condition of the mean value theorem However if you know only the less general version you could say, that $f$ has the MVT on every closed sub-interval of $]-1,1[$. What about the theorems (see question above). Dec15 asked Condition of the mean value theorem Dec3 revised Does every differentiable function has an infliction point between a local maximum and minimum? added 156 characters in body Dec2 comment Does every differentiable function has an infliction point between a local maximum and minimum? Furthermore $x$ beeing a local extremum doesn't imply that $f''(x) \neq 0$ (only that $f'(x)=0$). Dec2 awarded Commentator Dec2 comment Does every differentiable function has an infliction point between a local maximum and minimum? Thanks. But in the non strict case, is the theorem true or is there another counterexample? Dec2 comment Does every differentiable function has an infliction point between a local maximum and minimum? This is not the definition of inflection point. It is just a neccesary condition if $f$ is twice differentiable. It would be a sufficient condition for example if $f$ is three times differentiable and additionally $f'''(x) \neq 0$.