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If is a function, let us call a restriction of to . Let’s analyze one nice and pretty surprising fact concerning restrictions. Fact: Suppose we have a function of two variables and it’s restriction to every straight line going through … Continue reading
It is not difficult to prove that every continuously differentiable function : Must have a minumum point between two maximums and – If it has precisely one critical point, be it a local minimum or a local maximum, that point must also be a … Continue reading
This post is about the monster of the monsters, Riemann’s continuous almost nowhere differentiable function: Proving that it is continuous is simple enough; proving that it doesn’t have the derivative almost everywhere is more complicated. (It is differentiable on a … Continue reading
Here is a funny function that I could’t wrap my mind around as a freshman: if , and . It is both continuous and differentiable, the derivative at zero is 1, because: but at the same time – and that is … Continue reading