Question

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

score 100 · Answer 1 · 2019-04-12 01:25:33

100

Views

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

Published on 12 Apr 2019 - 1:25

score 96 · Answer 2 · 2019-04-18 13:56:51

96

Views

Generalization of Rolle's Theorem

Published on 18 Apr 2019 - 13:56

score 39 · Answer 3 · 2019-04-21 23:47:05

39

Views

a Mean Value Theorem Proof

Published on 21 Apr 2019 - 23:47

score 231 · Answer 4 · 2019-04-27 14:52:09

231

Views

Geometry of mean value theorem?

Published on 27 Apr 2019 - 14:52

score 968 · Answer 5 · 2019-05-15 13:12:37

968

Views

Root multiplicity for non-polynomial function

Published on 15 May 2019 - 13:12

score 123 · Answer 6 · 2019-05-16 22:39:53

123

Views

Rolle's and Lagrange's theorems in parametric equations

Published on 16 May 2019 - 22:39

score 70 · Answer 7 · 2019-05-27 20:21:34

70

Views

A function $g(x)$ has one and only one real root if $g'(x)\leq k <0$.

Published on 27 May 2019 - 20:21

score 248 · Answer 8 · 2019-06-05 08:32:29

248

Views

Given $f(x) = x \sin\frac1x$, find roots of $f'(x)$ in the interval $0\le x \le \frac 1{\pi}$.

Published on 05 Jun 2019 - 8:32

score 329 · Answer 9 · 2019-06-20 05:11:27

329

Views

Spivak, Calculus 3rd Ed. Chapter 11 problem 32

Published on 20 Jun 2019 - 5:11

score 124 · Answer 10 · 2019-06-28 12:07:36

124

Views

Some property of differentiable function

Published on 28 Jun 2019 - 12:07

score 133 · Answer 11 · 2019-07-03 21:47:19

133

Views

Rolle's theorem proof in Apostol: meaningfulness of interior

Published on 03 Jul 2019 - 21:47

score 340 · Answer 12 · 2019-07-24 14:42:39

340

Views

Application of Rolle's theorem and determinant

Published on 24 Jul 2019 - 14:42

score 56 · Answer 13 · 2019-08-28 23:27:27

56

Views

Is this inference from Rolle's Theorem correct?

Published on 28 Aug 2019 - 23:27

score 891 · Answer 14 · 2019-09-06 07:13:03

891

Views

Twice differentiable function on the closed interval $[a,b]$

Published on 06 Sep 2019 - 7:13

score 351 · Answer 15 · 2019-09-12 19:31:58

Let a function f(x) be twice differentiable such that $ f(0) = 0, f(\pi/2)= 1 , f(3\pi/2)=-1$. To prove that there exists a ‘c’ in $ (0,3\pi/2)$

List Question

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

Generalization of Rolle's Theorem

a Mean Value Theorem Proof

Geometry of mean value theorem?

Root multiplicity for non-polynomial function

Rolle's and Lagrange's theorems in parametric equations

A function $g(x)$ has one and only one real root if $g'(x)\leq k <0$.

Given $f(x) = x \sin\frac1x$, find roots of $f'(x)$ in the interval $0\le x \le \frac 1{\pi}$.

Spivak, Calculus 3rd Ed. Chapter 11 problem 32

Some property of differentiable function

Rolle's theorem proof in Apostol: meaningfulness of interior

Application of Rolle's theorem and determinant

Is this inference from Rolle's Theorem correct?

Twice differentiable function on the closed interval $[a,b]$

Let a function f(x) be twice differentiable such that $ f(0) = 0, f(\pi/2)= 1 , f(3\pi/2)=-1$. To prove that there exists a ‘c’ in $ (0,3\pi/2)$

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