Question

Let $f(x)$ be non-constant, twice differentiable function define on $\mathbb R$ such that $y=f(x)$ is symmetric about line $x=1$

score 418 · Answer 1 · 2022-01-12 11:48:35

418

Views

Let $f(x)$ be non-constant, twice differentiable function define on $\mathbb R$ such that $y=f(x)$ is symmetric about line $x=1$

Published on 12 Jan 2022 - 11:48

score 60 · Answer 2 · 2022-01-13 14:40:01

60

Views

Derivative at end point of a interval

Published on 13 Jan 2022 - 14:40

score 133 · Answer 3 · 2022-01-16 13:41:12

133

Views

Rolle's Theorem and error bound formula for trapezoidal rule

Published on 16 Jan 2022 - 13:41

score 91 · Answer 4 · 2026-02-24 03:30:41

91

Views

Sum of roots for a even function and slope being 0?

Published on 24 Feb 2026 - 3:30

score 75 · Answer 5 · 2022-01-24 20:27:23

75

Views

How do I determine further solutions of the equation using Rolle's theorem?

Published on 24 Jan 2022 - 20:27

score 61 · Answer 6 · 2022-02-05 07:43:17

61

Views

Differential calculus using Rolles theorem and mean value theorem

Published on 05 Feb 2022 - 7:43

score 141 · Answer 7 · 2022-02-07 13:08:56

141

Views

Showing there exists $\zeta$ such that $f(\zeta)=f'(\zeta)$ by Rolle's theorem: motivating the definition of an auxiliary function

Published on 07 Feb 2022 - 13:08

score 131 · Answer 8 · 2022-02-07 21:32:20

131

Views

If $3a+2b+3c=0,$ show that the cubic polynomial $ax^3+bx+c$ has at least one root in the interval $(0,2)$

Published on 07 Feb 2022 - 21:32

score 165 · Answer 9 · 2022-02-21 10:36:11

165

Views

Number of roots of $2013x^{2012}-2012x^{2011}-16x+8=0$ in $[0,8^\frac1{2011}]$

Published on 21 Feb 2022 - 10:36

score 718 · Answer 10 · 2022-03-15 23:16:30

718

Views

$f:[a,b]\to\mathbb{R}$ continuous function and differentiable in (a,b) $\rightarrow$ $\exists$ $c\in(a,b)$ with $f(c)=\frac{1}{a-c}+\frac{1}{b-c}$

Published on 15 Mar 2022 - 23:16

score 111 · Answer 11 · 2022-03-17 12:39:29

111

Views

Finding the number of real roots of a polynomial

Published on 17 Mar 2022 - 12:39

score 72 · Answer 12 · 2022-03-30 15:14:17

72

Views

If $f(x)\rightarrow L$ from both sides then $f'(c)=0$ for some $c$

Published on 30 Mar 2022 - 15:14

score 534 · Answer 13 · 2022-04-19 11:56:28

534

Views

Let $a$ be an integer such that all real roots of the polynomial $2x^5+5x^4+10x^3+10x^2+10x+10$ lie in the interval $(a,a+1)$

Published on 19 Apr 2022 - 11:56

score 70 · Answer 14 · 2022-04-20 00:43:33

70

Views

Proof checking for Rolles Theorem

Published on 20 Apr 2022 - 0:43

score 54 · Answer 15 · 2022-05-07 00:40:42

54

Views

Rolles theorem: differentiabilty open brackets significance

Published on 07 May 2022 - 0:40

List Question

Let $f(x)$ be non-constant, twice differentiable function define on $\mathbb R$ such that $y=f(x)$ is symmetric about line $x=1$

Derivative at end point of a interval

Rolle's Theorem and error bound formula for trapezoidal rule

Sum of roots for a even function and slope being 0?

How do I determine further solutions of the equation using Rolle's theorem?

Differential calculus using Rolles theorem and mean value theorem

Showing there exists $\zeta$ such that $f(\zeta)=f'(\zeta)$ by Rolle's theorem: motivating the definition of an auxiliary function

If $3a+2b+3c=0,$ show that the cubic polynomial $ax^3+bx+c$ has at least one root in the interval $(0,2)$

Number of roots of $2013x^{2012}-2012x^{2011}-16x+8=0$ in $[0,8^\frac1{2011}]$

$f:[a,b]\to\mathbb{R}$ continuous function and differentiable in (a,b) $\rightarrow$ $\exists$ $c\in(a,b)$ with $f(c)=\frac{1}{a-c}+\frac{1}{b-c}$

Finding the number of real roots of a polynomial

If $f(x)\rightarrow L$ from both sides then $f'(c)=0$ for some $c$

Let $a$ be an integer such that all real roots of the polynomial $2x^5+5x^4+10x^3+10x^2+10x+10$ lie in the interval $(a,a+1)$

Proof checking for Rolles Theorem

Rolles theorem: differentiabilty open brackets significance

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