Question

Is Rolle's theorem and Mean values theorem same?

score 440 · Answer 1 · 2021-07-09 06:05:20

440

Views

Is Rolle's theorem and Mean values theorem same?

Published on 09 Jul 2021 - 6:05

score 183 · Answer 2 · 2021-07-10 03:58:08

183

Views

Rules of checking differentiability for Rolle's theorem

Published on 10 Jul 2021 - 3:58

score 110 · Answer 3 · 2021-07-10 06:22:23

110

Views

Verify Rolle's theorem

Published on 10 Jul 2021 - 6:22

score 97 · Answer 4 · 2021-07-11 03:46:43

97

Views

$f(x) = (x^2 -1)^2(a_0 x^3+a_1 x^2 + a_2 x + a_3 )$ $f'(x)$ has exactly $3$ distinct real roots and $f''(x)$ has two distinct real roots. Find $f(x)$.

Published on 11 Jul 2021 - 3:46

score 106 · Answer 5 · 2021-07-31 22:23:57

106

Views

If $f$ is twice differentiable such that $f\left(\frac{1}{n}\right)=0$, then what can we say about $f''(0)$?

Published on 31 Jul 2021 - 22:23

score 47 · Answer 6 · 2021-08-15 10:29:59

47

Views

Interval in which roots of given function lies is:

Published on 15 Aug 2021 - 10:29

score 124 · Answer 7 · 2021-08-24 09:16:15

124

Views

Solving the equation of the type $g\left( x \right) = \int\limits_0^x {f\left( t \right)dt} $

Published on 24 Aug 2021 - 9:16

score 153 · Answer 8 · 2021-09-09 14:15:55

153

Views

Prove that the polynomial has exactly 2 real roots by IVT or Rolle's Theorem

Published on 09 Sep 2021 - 14:15

score 158 · Answer 9 · 2021-09-10 22:47:07

158

Views

If $P_n(x)$ has n real roots, then it's derivative has no complex roots

Published on 10 Sep 2021 - 22:47

score 1.6k · Answer 10 · 2021-09-20 01:54:51

1.6k

Views

Let $f$ be a continuous function in $[0,5]$ and twice differentiable function in $(0,5)$ such that $f(4)=f(5)=0$. Prove the following

Published on 20 Sep 2021 - 1:54

score 43 · Answer 11 · 2021-10-04 16:32:53

43

Views

Mean value theorem to prove existence of zero for second derivative

Published on 04 Oct 2021 - 16:32

score 317 · Answer 12 · 2021-10-05 16:02:46

317

Views

Prove there exists a point $\xi$ so that $f'(\xi)=0$

Published on 05 Oct 2021 - 16:02

score 88 · Answer 13 · 2021-10-17 03:10:39

88

Views

Existence of $x_0 \in (0,1)$, s.t. $f'(x_0)+1/x_0 f(x_0)=2$

Published on 17 Oct 2021 - 3:10

score 107 · Answer 14 · 2021-12-31 15:05:54

107

Views

Problem involving Rolle's Theorem

Published on 31 Dec 2021 - 15:05

score 23 · Answer 15 · 2022-01-05 16:54:16

23

Views

Is it possible to show the following without the assumption of continuity in a closed inteval?

Published on 05 Jan 2022 - 16:54

List Question

Is Rolle's theorem and Mean values theorem same?

Rules of checking differentiability for Rolle's theorem

Verify Rolle's theorem

$f(x) = (x^2 -1)^2(a_0 x^3+a_1 x^2 + a_2 x + a_3 )$ $f'(x)$ has exactly $3$ distinct real roots and $f''(x)$ has two distinct real roots. Find $f(x)$.

If $f$ is twice differentiable such that $f\left(\frac{1}{n}\right)=0$, then what can we say about $f''(0)$?

Interval in which roots of given function lies is:

Solving the equation of the type $g\left( x \right) = \int\limits_0^x {f\left( t \right)dt} $

Prove that the polynomial has exactly 2 real roots by IVT or Rolle's Theorem

If $P_n(x)$ has n real roots, then it's derivative has no complex roots

Let $f$ be a continuous function in $[0,5]$ and twice differentiable function in $(0,5)$ such that $f(4)=f(5)=0$. Prove the following

Mean value theorem to prove existence of zero for second derivative

Prove there exists a point $\xi$ so that $f'(\xi)=0$

Existence of $x_0 \in (0,1)$, s.t. $f'(x_0)+1/x_0 f(x_0)=2$

Problem involving Rolle's Theorem

Is it possible to show the following without the assumption of continuity in a closed inteval?

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