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visits member for 2 years, 10 months
seen Dec 16 at 13:41

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
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
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 $f'''(x) \neq 0$.
Oct
19
comment Asymptote of solution of a differential equation without solving it
I don't really understand why it is sufficient to show that $u'(x) > 0$ for all $x$ and why this it the case. If $u'(x_0) = 0$ for some $x_0$, why is this automatically the case for all $x$?
Oct
15
comment Intiutive argument that $\exp' = \exp$
@mookid It's for a high school course. The real numbers are known only on a heuristic middle school level (via examples like $\sqrt{2}$ and $\pi$, nested intervals etc. Powers are introduced usually just for rational numbers and real powers via nested intervals (or sometimes just with reference to the calculater - which is really sad, but I don't have the time to rework those foundations, I just want to give a nice argument for the derivative of $\exp$ despite of the spongy foundations :-()
Oct
15
comment Intiutive argument that $\exp' = \exp$
But how to show that $\exp'(0) = 1$?
Jul
24
comment Asymptote of solution of a differential equation without solving it
Would be nice if you could make it more rigerous
May
9
comment Proof: Force always perpendicular and motion in a plane implies that the trajectory is a circle
@DanielV No I mean that the force which corresponds to $x''$ and $x'$ which corresponds to the velocity are perpendicular.
Mar
15
comment Real world applications of exponential function; continous case
Well that's clear. The point is just that I cannot assume that students are familiar with $\mathrm{e}$.
Mar
15
comment Real world applications of exponential function; continous case
@mookid Yes but thats for the case $b < 1$, it's a decay. I know there are many interesting (quasi-)continous examples with $b < 1$, but I didn't know any really interesting examples for $b > 1$ which are not discrete.
Sep
21
comment Reference for similarity tests for triangles
Thanks for nice link! However it would be better to have a book as a reference since I want to cite it. By the way the link is about congruence, my question was about similarity.