List questions from mean-value-theorem

Published on 27 Dec 2023 - 15:10

147

Views

Let $f$ be continuous in $[0,2]$ and differentiable in $(0,2)$ such that $|f'(x)|\leqslant1$ and $f(0)=1=f(2)$. Prove that $f(x)\geqslant0$.

Published on 23 Feb 2026 - 20:04

51

Views

How to prove that a 2D function f(x,y) is always equal to a 1D function g(x) if f(x,y) always has zero gradient in the y direction

Published on 03 Jan 2024 - 16:51

88

Views

For a differentiable function $f$ , does this mean value theorem iteration method converge to the root of $f?$

Published on 05 Jan 2024 - 14:48

110

Views

Alternative solution for integral limit using mean theorem

Published on 12 Jan 2024 - 22:42

124

Views

Which function is differentiable on $[a,b]$ but doesn't reach an extreme on $[a,b]$?

Published on 17 Jan 2024 - 7:00

56

Views

On connected sets of $\mathbb{R}^{n}$.

Published on 19 Jan 2024 - 1:15

124

Views

$f(x)$ has 3 distinct solutions on $[a,b]$ and $f(x)$ has a continuous second derivative on $[a,b]$, then $f''(x)+2f(x)$ has solutions on $[a,b]$

Published on 24 Jan 2024 - 14:28

130

Views

Integral inequality : for $f\in C^{4}[0,1]$ with $f(0)=f(1)=f^\prime(0)=f^\prime(1)=0$, show that $\int_0^1|\frac{f^{(4)}(x)}{f(x)}|dx\geq 192$

Published on 27 Jan 2024 - 6:21

43

Views

Taylor expansion to reformulate difference of function at two points

Published on 28 Jan 2024 - 22:20

32

Views

Counter example: continuity assumption of mean value theorem

Published on 29 Jan 2024 - 14:55

35

Views

$f(U)$ is an interval of length $\leq 3m$.

Published on 30 Jan 2024 - 5:34

120

Views

A Detail in Mean Value Theorem for Integrals

Published on 01 Feb 2024 - 4:54

46

Views

Find sufficient condition for having $f(x)>0$

Published on 07 Feb 2024 - 17:32

89

Views

Use the MVT for Integrals to bound $\int_0^1\frac{x^6}{\sqrt{1+x^2}}dx$

Published on 12 Feb 2024 - 17:00

List Question

Derivative Function

Let $f$ be continuous in $[0,2]$ and differentiable in $(0,2)$ such that $|f'(x)|\leqslant1$ and $f(0)=1=f(2)$. Prove that $f(x)\geqslant0$.

How to prove that a 2D function f(x,y) is always equal to a 1D function g(x) if f(x,y) always has zero gradient in the y direction

For a differentiable function $f$ , does this mean value theorem iteration method converge to the root of $f?$

Alternative solution for integral limit using mean theorem

Which function is differentiable on $[a,b]$ but doesn't reach an extreme on $[a,b]$?

On connected sets of $\mathbb{R}^{n}$.

$f(x)$ has 3 distinct solutions on $[a,b]$ and $f(x)$ has a continuous second derivative on $[a,b]$, then $f''(x)+2f(x)$ has solutions on $[a,b]$

Integral inequality : for $f\in C^{4}[0,1]$ with $f(0)=f(1)=f^\prime(0)=f^\prime(1)=0$, show that $\int_0^1|\frac{f^{(4)}(x)}{f(x)}|dx\geq 192$

Taylor expansion to reformulate difference of function at two points

Counter example: continuity assumption of mean value theorem

$f(U)$ is an interval of length $\leq 3m$.

A Detail in Mean Value Theorem for Integrals

Find sufficient condition for having $f(x)>0$

Use the MVT for Integrals to bound $\int_0^1\frac{x^6}{\sqrt{1+x^2}}dx$

Trending Questions

Popular # Hahtags

Popular Questions