Question

If you have an inflection point, is there a three-term A.P. in the domain that the function maps to a three-term A.P.?

score 56 · Answer 1 · 2023-04-30 20:17:10

56

Views

If you have an inflection point, is there a three-term A.P. in the domain that the function maps to a three-term A.P.?

Published on 30 Apr 2023 - 20:17

score 72 · Answer 2 · 2023-05-01 11:16:47

72

Views

How can I show that $|e^{2x} - e^{2y}| \leq 8|x - y|$ for all $x < y < \ln{2}$?

Published on 01 May 2023 - 11:16

score 142 · Answer 3 · 2023-05-10 13:15:11

142

Views

Mean-value theorem for function of matrices

Published on 10 May 2023 - 13:15

score 148 · Answer 4 · 2023-05-12 17:26:02

148

Views

Find the value of $\sqrt[3]{26}$ using Mean Value Theorem

Published on 12 May 2023 - 17:26

score 61 · Answer 5 · 2023-05-13 04:42:03

61

Views

Let $f(x) = x^5 + x^3 +2x +1$ and let $g$ be its inverse. Let $a,b \in\mathbb R$ with $a < b$. Show that $g(b) − g(a) \le 0.5(b −a)$

Published on 13 May 2023 - 4:42

score 60 · Answer 6 · 2023-05-13 22:42:48

60

Views

Mean Value theorem for inequalities

Published on 13 May 2023 - 22:42

score 206 · Answer 7 · 2023-05-15 17:15:13

206

Views

Integral divides Integral

Published on 15 May 2023 - 17:15

score 421 · Answer 8 · 2023-05-16 06:47:28

421

Views

Show there exists $c\in(0,1)$ such that $\frac{f'(1-c)}{f(1-c)}=\frac{2f'(c)}{f(c)}$

Published on 16 May 2023 - 6:47

score 39 · Answer 9 · 2023-05-16 09:46:44

In L'Hospital rule should we specify $g(x) \ne 0$ on $(a,b)$ in the theorem to avoid division by $0$? Does $g'(x)\ne 0$ imply $g(x)\ne 0$ on $(a,b)$?

score 54 · Answer 10 · 2023-05-18 16:52:52

54

Views

True or false: If $f(0)=0$ and $f(1)=1$ , then there exist distinct $a,b\in (0,1)$ such that $f'(a)+f'(b)=2$

Published on 18 May 2023 - 16:52

score 52 · Answer 11 · 2023-05-20 06:11:23

52

Views

If $f=g'$ for continuous $g$, then Fundamental Theorem of Calculus works

Published on 20 May 2023 - 6:11

score 95 · Answer 12 · 2023-05-24 05:30:34

95

Views

Find an upper bound for $\int_{0}^{1}\cos(x)\frac{x f'(x) - f(x) + f(0)}{x^2}dx$

Published on 24 May 2023 - 5:30

score 91 · Answer 13 · 2023-05-24 12:54:34

91

Views

Proving an equality for $\int_{0}^{1}x^{4}f(x)\,dx$

Published on 24 May 2023 - 12:54

score 149 · Answer 14 · 2023-05-25 04:53:10

149

Views

$f : (a, b] \to \mathbb{R}$, where $f'(x)$ exists and bounded in $(a, b]$. Prove: $\lim_{x \to a^{+}}f(x)$ exists.

Published on 25 May 2023 - 4:53

score 74 · Answer 15 · 2023-05-30 22:50:48

74

Views

Solve problems of the form "given a differentiable function prove that there exists a point c such that"

Published on 30 May 2023 - 22:50

List Question

If you have an inflection point, is there a three-term A.P. in the domain that the function maps to a three-term A.P.?

How can I show that $|e^{2x} - e^{2y}| \leq 8|x - y|$ for all $x < y < \ln{2}$?

Mean-value theorem for function of matrices

Find the value of $\sqrt[3]{26}$ using Mean Value Theorem

Let $f(x) = x^5 + x^3 +2x +1$ and let $g$ be its inverse. Let $a,b \in\mathbb R$ with $a < b$. Show that $g(b) − g(a) \le 0.5(b −a)$

Mean Value theorem for inequalities

Integral divides Integral

Show there exists $c\in(0,1)$ such that $\frac{f'(1-c)}{f(1-c)}=\frac{2f'(c)}{f(c)}$

In L'Hospital rule should we specify $g(x) \ne 0$ on $(a,b)$ in the theorem to avoid division by $0$? Does $g'(x)\ne 0$ imply $g(x)\ne 0$ on $(a,b)$?

True or false: If $f(0)=0$ and $f(1)=1$ , then there exist distinct $a,b\in (0,1)$ such that $f'(a)+f'(b)=2$

If $f=g'$ for continuous $g$, then Fundamental Theorem of Calculus works

Find an upper bound for $\int_{0}^{1}\cos(x)\frac{x f'(x) - f(x) + f(0)}{x^2}dx$

Proving an equality for $\int_{0}^{1}x^{4}f(x)\,dx$

$f : (a, b] \to \mathbb{R}$, where $f'(x)$ exists and bounded in $(a, b]$. Prove: $\lim_{x \to a^{+}}f(x)$ exists.

Solve problems of the form "given a differentiable function prove that there exists a point c such that"

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