List questions from monotone-functions

Published on 04 May 2020 - 11:40

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Why is $n^n = O(2^{n^c})$?

Published on 21 Mar 2026 - 17:06

124

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Existence of a monotonic function that is not differentiable anywhere

Published on 25 Mar 2026 - 16:01

67

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Show strict monotony and convexity for given function

Published on 06 May 2020 - 21:09

32

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If X and Y are i.i.d and positive, is Pr(X + Y < x|X < x) increasing in x?

Published on 25 Mar 2026 - 22:05

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If $f(2x)=f(x)+f(2), \forall x > 1$ prove that $f$ in increasing

Published on 12 May 2020 - 12:30

265

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A monotone function $f$ on $[0,1]$ satisfying $f\big(\frac14\big)f\big(\frac34\big)\lt 0$

Published on 14 May 2020 - 7:35

48

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Decomposition of a polynomial function $f:[a,b]\to \mathbb{R}$ as the sum of two monotonous functions.

Published on 14 May 2020 - 17:37

637

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Is the derivative always nonnegative in a neighbourhood of a minimum?

Published on 15 May 2020 - 5:02

200

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Monotonic function without asymptote

Published on 15 May 2020 - 20:41

1.1k

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How do we prove that strictly monotone continuous functions admit strictly monotone increasing continuous inverse?

Published on 16 May 2020 - 21:55

47

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How to show this one is monotone?

Published on 19 May 2020 - 7:07

41

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Prove that a sequence decreases monotonically

Published on 23 May 2020 - 2:43

75

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Monotony of $f(x)=x+x^2\sin(\frac{1}{x})+1$ (Prove $f$ is strictly increasing)

Published on 25 May 2020 - 7:59

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The modulus of Gamma function $\left| \Gamma(x+iy) \right|$ is strictly decreasing when $x \in (0,\frac{1}{2})$ for a fixed $y \in \mathbb{R_+}$

Published on 25 May 2020 - 19:32

List Question

Exercise on monotone functions

Why is $n^n = O(2^{n^c})$?

Existence of a monotonic function that is not differentiable anywhere

Show strict monotony and convexity for given function

If X and Y are i.i.d and positive, is Pr(X + Y < x|X < x) increasing in x?

If $f(2x)=f(x)+f(2), \forall x > 1$ prove that $f$ in increasing

A monotone function $f$ on $[0,1]$ satisfying $f\big(\frac14\big)f\big(\frac34\big)\lt 0$

Decomposition of a polynomial function $f:[a,b]\to \mathbb{R}$ as the sum of two monotonous functions.

Is the derivative always nonnegative in a neighbourhood of a minimum?

Monotonic function without asymptote

How do we prove that strictly monotone continuous functions admit strictly monotone increasing continuous inverse?

How to show this one is monotone?

Prove that a sequence decreases monotonically

Monotony of $f(x)=x+x^2\sin(\frac{1}{x})+1$ (Prove $f$ is strictly increasing)

The modulus of Gamma function $\left| \Gamma(x+iy) \right|$ is strictly decreasing when $x \in (0,\frac{1}{2})$ for a fixed $y \in \mathbb{R_+}$

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