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Mar
19
comment Define the Riemann integral via trapezoids instead of rectangles
Yes I am still interested.
Mar
17
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.
Mar
17
comment Define the Riemann integral via trapezoids instead of rectangles
Thanks. Can you give more details for the nontrivial direction of the equivalence?
Mar
17
revised Define the Riemann integral via trapezoids instead of rectangles
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Mar
16
comment Define the Riemann integral via trapezoids instead of rectangles
Thanks for the idea. How to get it for general functions?
Mar
16
asked Define the Riemann integral via trapezoids instead of rectangles
Feb
11
revised Continuity of third derivative in extremum test
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Feb
10
revised Continuity of third derivative in extremum test
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Feb
10
comment Continuity of third derivative in extremum test
@rubik Just the topological interior of $I$.
Feb
10
asked Continuity of third derivative in extremum test
Jan
5
awarded  Popular Question
Dec
15
awarded  Caucus
Dec
15
revised Condition of the mean value theorem
edited tags
Dec
15
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).
Dec
15
asked Condition of the mean value theorem
Dec
3
revised Does every differentiable function has an infliction point between a local maximum and minimum?
added 156 characters in body
Dec
2
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 $f'(x)=0$).
Dec
2
awarded  Commentator
Dec
2
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?
Dec
2
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 $f'''(x) \neq 0$.