Question

If $f$ is $C^1$ s. t. $\Vert f(x) - f(y) \Vert \geq k \Vert x - y \Vert$, then $f$ is a diffeomorphism of $\mathbb{R}^{n}$

score 201 · Answer 1 · 2026-05-10 15:47:45

201

Views

If $f$ is $C^1$ s. t. $\Vert f(x) - f(y) \Vert \geq k \Vert x - y \Vert$, then $f$ is a diffeomorphism of $\mathbb{R}^{n}$

Published on 10 May 2026 - 15:47

score 40 · Answer 2 · 2026-04-12 13:17:27

40

Views

Prove this formula follows from a function being continuously differentiable?

Published on 12 Apr 2026 - 13:17

score 75 · Answer 3 · 2026-04-16 00:48:16

75

Views

$\frac 1 {\overline {f(1/\ \overline z)}}$ is differentiable for $|z|>1$

Published on 16 Apr 2026 - 0:48

score 33 · Answer 4 · 2026-04-11 20:04:19

33

Views

How to show that the labour supply curve will not be negatively sloped?

Published on 11 Apr 2026 - 20:04

score 37 · Answer 5 · 2026-04-17 08:15:43

37

Views

Show that $g=f\mid_{B_{1}(0)}$ is injective and determines the range of $g$ where $f(x) = \Vert x \Vert^{2}x$

Published on 17 Apr 2026 - 8:15

score 58 · Answer 6 · 2026-04-14 16:03:12

58

Views

How to prove that there exists two distinct points $c$ and $d$ such that $f'(c)f'(d)=1$ where $f$ is continuous on [a,b]

Published on 14 Apr 2026 - 16:03

score 53 · Answer 7 · 2026-04-15 15:38:56

53

Views

Are the graphs I sketched of the derivative of a function and the function correct?

Published on 15 Apr 2026 - 15:38

score 314 · Answer 8 · 2026-04-14 09:08:46

314

Views

Square integrable first derivative and second-order differentiability

Published on 14 Apr 2026 - 9:08

score 46 · Answer 9 · 2026-04-16 23:54:09

46

Views

If $D_{x_{0}}f$ is an isomorphism, there is $V_{x_{0}}$ s.t. $f(x) \neq f(x_{0})$ for $x \in V_{x_{0}}-\{x_{0}\}$.

Published on 16 Apr 2026 - 23:54

score 84 · Answer 10 · 2026-04-11 14:23:09

84

Views

Derivative of a function with summation

Published on 11 Apr 2026 - 14:23

score 337 · Answer 11 · 2026-04-17 08:41:35

337

Views

In the derivative of the product of two functions , why (dx)² is ignored?

Published on 17 Apr 2026 - 8:41

score 52 · Answer 12 · 2026-04-11 02:03:45

52

Views

What precisely does the notation $\frac {\partial h} {\partial z}$ mean in this context?

Published on 11 Apr 2026 - 2:03

score 41 · Answer 13 · 2026-04-12 19:23:11

41

Views

Calc2 Finding $f'(2)$ from tangent line

Published on 12 Apr 2026 - 19:23

score 4.1k · Answer 14 · 2026-04-10 06:03:25

4.1k

Views

What is the difference between a derivative and a differential equation?

Published on 10 Apr 2026 - 6:03

score 1k · Answer 15 · 2026-04-10 19:27:10

1k

Views

The derivative of an integral of a product of functions.

Published on 10 Apr 2026 - 19:27

List Question

If $f$ is $C^1$ s. t. $\Vert f(x) - f(y) \Vert \geq k \Vert x - y \Vert$, then $f$ is a diffeomorphism of $\mathbb{R}^{n}$

Prove this formula follows from a function being continuously differentiable?

$\frac 1 {\overline {f(1/\ \overline z)}}$ is differentiable for $|z|>1$

How to show that the labour supply curve will not be negatively sloped?

Show that $g=f\mid_{B_{1}(0)}$ is injective and determines the range of $g$ where $f(x) = \Vert x \Vert^{2}x$

How to prove that there exists two distinct points $c$ and $d$ such that $f'(c)f'(d)=1$ where $f$ is continuous on [a,b]

Are the graphs I sketched of the derivative of a function and the function correct?

Square integrable first derivative and second-order differentiability

If $D_{x_{0}}f$ is an isomorphism, there is $V_{x_{0}}$ s.t. $f(x) \neq f(x_{0})$ for $x \in V_{x_{0}}-\{x_{0}\}$.

Derivative of a function with summation

In the derivative of the product of two functions , why (dx)² is ignored?

What precisely does the notation $\frac {\partial h} {\partial z}$ mean in this context?

Calc2 Finding $f'(2)$ from tangent line

What is the difference between a derivative and a differential equation?

The derivative of an integral of a product of functions.

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