Question

Monotonic Functions

score 68 · Answer 1 · 2020-01-28 10:14:27

68

Views

Monotonic Functions

Published on 28 Jan 2020 - 10:14

score 159 · Answer 2 · 2020-01-28 13:11:37

159

Views

A question about the definition of a strictly increasing function

Published on 28 Jan 2020 - 13:11

score 375 · Answer 3 · 2020-02-04 20:57:14

375

Views

How to prove monotonicity in this case?

Published on 04 Feb 2020 - 20:57

score 96 · Answer 4 · 2020-02-05 14:38:54

96

Views

Show that f is not an increasing function on any neighbourhood of 0.

Published on 05 Feb 2020 - 14:38

score 69 · Answer 5 · 2020-02-08 17:31:57

69

Views

Is a one-one non-decreasing function always increasing?

Published on 08 Feb 2020 - 17:31

score 1k · Answer 6 · 2020-02-10 03:22:56

1k

Views

Composition of monotonic functions

Published on 10 Feb 2020 - 3:22

score 80 · Answer 7 · 2020-02-13 18:20:22

80

Views

Regarding point of inflection

Published on 13 Feb 2020 - 18:20

score 2.1k · Answer 8 · 2020-02-13 21:10:14

2.1k

Views

For every twice differentiable function $f : \bf R \rightarrow [–2, 2]$ with $(f(0))^2 + (f'(0))^2 = 85$, which of the following statements are TRUE?

Published on 13 Feb 2020 - 21:10

score 60 · Answer 9 · 2026-03-25 11:12:39

60

Views

Intuition for complete monotne functions

Published on 25 Mar 2026 - 11:12

score 362 · Answer 10 · 2020-02-18 09:25:50

362

Views

$f(f(x)) = x \Longleftrightarrow f(x) = x$ if $f(x)$ is monotonically increasing. Can it work for monotonically decreasing $f(x)$ or $f(f(f(x)))$

Published on 18 Feb 2020 - 9:25

score 146 · Answer 11 · 2020-02-19 15:33:15

146

Views

Unique increasing function solution $y(x)$ such that $f_0(x) = f_1(y(x))$

Published on 19 Feb 2020 - 15:33

score 456 · Answer 12 · 2020-02-20 08:11:05

456

Views

$f$ is not monotonic if and only if there exist $a<b<c$ s.t. $f(a)>f(b)<f(c)$ or $f(a)<f(b)>f(c)$.

Published on 20 Feb 2020 - 8:11

score 252 · Answer 13 · 2026-03-22 15:24:42

252

Views

Interchange Argmin and Monotone Function

Published on 22 Mar 2026 - 15:24

score 36 · Answer 14 · 2020-02-21 20:05:30

36

Views

If $f(0) > g(0)$, and $\exists N > 0$ such that if $k\geq N$ then $f(k)>g(k)$ and $f,g$ are monotonic increasing, is $f(x)>g(x)$ $\forall x\geq 0$?

Published on 21 Feb 2020 - 20:05

score 261 · Answer 15 · 2026-03-25 09:48:19

261

Views

Unique increasing solution to a separable differential equation (piecewise $C_1$)

Published on 25 Mar 2026 - 9:48

List Question

Monotonic Functions

A question about the definition of a strictly increasing function

How to prove monotonicity in this case?

Show that f is not an increasing function on any neighbourhood of 0.

Is a one-one non-decreasing function always increasing?

Composition of monotonic functions

Regarding point of inflection

For every twice differentiable function $f : \bf R \rightarrow [–2, 2]$ with $(f(0))^2 + (f'(0))^2 = 85$, which of the following statements are TRUE?

Intuition for complete monotne functions

$f(f(x)) = x \Longleftrightarrow f(x) = x$ if $f(x)$ is monotonically increasing. Can it work for monotonically decreasing $f(x)$ or $f(f(f(x)))$

Unique increasing function solution $y(x)$ such that $f_0(x) = f_1(y(x))$

$f$ is not monotonic if and only if there exist $a<b<c$ s.t. $f(a)>f(b)<f(c)$ or $f(a)<f(b)>f(c)$.

Interchange Argmin and Monotone Function

If $f(0) > g(0)$, and $\exists N > 0$ such that if $k\geq N$ then $f(k)>g(k)$ and $f,g$ are monotonic increasing, is $f(x)>g(x)$ $\forall x\geq 0$?

Unique increasing solution to a separable differential equation (piecewise $C_1$)

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