Question

Minimum number of roots of a polynomial

score 732 · Answer 1 · 2026-02-24 02:27:29

732

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Minimum number of roots of a polynomial

Published on 24 Feb 2026 - 2:27

score 66 · Answer 2 · 2026-02-24 02:22:19

66

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Proving derivative has at least two roots

Published on 24 Feb 2026 - 2:22

score 116 · Answer 3 · 2026-02-24 02:20:49

116

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Checking increasing or decreasing function of twice differentiable function

Published on 24 Feb 2026 - 2:20

score 49 · Answer 4 · 2026-04-09 08:54:24

49

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Proof relating to mean Value Theorem

Published on 09 Apr 2026 - 8:54

score 88 · Answer 5 · 2026-02-24 02:24:36

88

Views

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

Published on 24 Feb 2026 - 2:24

score 86 · Answer 6 · 2026-02-24 02:28:34

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 · 2026-04-11 22:30:07

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 11 Apr 2026 - 22:30

score 88 · Answer 8 · 2026-02-24 02:23:48

88

Views

Proving a parabola and polynomial intersect exactly 3 times

Published on 24 Feb 2026 - 2:23

score 60 · Answer 9 · 2026-04-11 11:09:01

60

Views

Is this a correct application of Rolle's Theorem?

Published on 11 Apr 2026 - 11:09

score 61 · Answer 10 · 2026-04-11 16:58:22

61

Views

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

Published on 11 Apr 2026 - 16:58

score 819 · Answer 11 · 2026-02-24 02:27:08

819

Views

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

Published on 24 Feb 2026 - 2:27

score 39 · Answer 12 · 2026-02-24 02:28:34

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 76 · Answer 13 · 2026-04-09 12:58:40

76

Views

Applications of Rolle's Theorem and function analysis

Published on 09 Apr 2026 - 12:58

score 100 · Answer 14 · 2026-02-24 02:23:48

100

Views

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

Published on 24 Feb 2026 - 2:23

score 131 · Answer 15 · 2026-02-24 02:27:36

131

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 24 Feb 2026 - 2:27

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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