Question

Minimum number of roots of a polynomial

score 731 · Answer 1 · 2020-10-15 05:03:38

731

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Minimum number of roots of a polynomial

Published on 15 Oct 2020 - 5:03

score 65 · Answer 2 · 2020-10-15 07:31:44

65

Views

Proving derivative has at least two roots

Published on 15 Oct 2020 - 7:31

score 115 · Answer 3 · 2020-10-17 06:27:16

115

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Checking increasing or decreasing function of twice differentiable function

Published on 17 Oct 2020 - 6:27

score 46 · Answer 4 · 2020-10-17 16:02:36

46

Views

Proof relating to mean Value Theorem

Published on 17 Oct 2020 - 16:02

score 87 · Answer 5 · 2020-10-19 06:53:33

87

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Prove a continuous function $f : [-1,1] \to \mathbb{R}$ has at least two roots in $(-1,1)$ given two integral values

Published on 19 Oct 2020 - 6:53

score 85 · Answer 6 · 2020-10-23 06:24:47

Let $f(x)=\begin{cases} x^a\ln x & x>0 \\ 0 & x=0 \end{cases}$. Find the value of $a$ for which Rolle’s theorem is applicable in $[0,1]$

score 1.2k · Answer 7 · 2026-02-23 20:59:27

1.2k

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For fundamental solutions $y_1,y_2$, there exist one and only one zero of $y_1$ between consecutive zeros of $y_2$.

Published on 23 Feb 2026 - 20:59

score 87 · Answer 8 · 2020-11-22 11:50:38

87

Views

Proving a parabola and polynomial intersect exactly 3 times

Published on 22 Nov 2020 - 11:50

score 58 · Answer 9 · 2020-11-29 13:31:13

58

Views

Is this a correct application of Rolle's Theorem?

Published on 29 Nov 2020 - 13:31

score 59 · Answer 10 · 2020-12-04 16:13:46

59

Views

A problem to prove $f'(c)$ as a sum of the given elements as in problem

Published on 04 Dec 2020 - 16:13

score 818 · Answer 11 · 2020-12-06 21:43:37

818

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f is continuous on [0,1]. f(0) = f(1). Show that f'(1 - c) = f'(c)

Published on 06 Dec 2020 - 21:43

score 38 · Answer 12 · 2020-12-08 01:14:08

Let $f: [0,6] \rightarrow \mathbb R$ be a three times differentiable function such that $f(0)=f(1.4)=f(3.9)=f(5.2)$.

score 73 · Answer 13 · 2020-12-21 09:45:03

73

Views

Applications of Rolle's Theorem and function analysis

Published on 21 Dec 2020 - 9:45

score 99 · Answer 14 · 2020-12-22 07:29:12

99

Views

If the derivative tends to $0$ at infinity, then so does the function divided by $x$

Published on 22 Dec 2020 - 7:29

score 130 · Answer 15 · 2020-12-25 07:29:28

130

Views

$f(x)=(x-2)(x-7)(x-9)(x-12)$ how many roots is there to $f'(x)=0$ and $f''(x)=0$? without taking derivative.

Published on 25 Dec 2020 - 7:29

List Question

Minimum number of roots of a polynomial

Proving derivative has at least two roots

Checking increasing or decreasing function of twice differentiable function

Proof relating to mean Value Theorem

Prove a continuous function $f : [-1,1] \to \mathbb{R}$ has at least two roots in $(-1,1)$ given two integral values

Let $f(x)=\begin{cases} x^a\ln x & x>0 \\ 0 & x=0 \end{cases}$. Find the value of $a$ for which Rolle’s theorem is applicable in $[0,1]$

For fundamental solutions $y_1,y_2$, there exist one and only one zero of $y_1$ between consecutive zeros of $y_2$.

Proving a parabola and polynomial intersect exactly 3 times

Is this a correct application of Rolle's Theorem?

A problem to prove $f'(c)$ as a sum of the given elements as in problem

f is continuous on [0,1]. f(0) = f(1). Show that f'(1 - c) = f'(c)

Let $f: [0,6] \rightarrow \mathbb R$ be a three times differentiable function such that $f(0)=f(1.4)=f(3.9)=f(5.2)$.

Applications of Rolle's Theorem and function analysis

If the derivative tends to $0$ at infinity, then so does the function divided by $x$

$f(x)=(x-2)(x-7)(x-9)(x-12)$ how many roots is there to $f'(x)=0$ and $f''(x)=0$? without taking derivative.

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