Question

A function with a point of slope of exactly $2$

score 99 · Answer 1 · 2019-12-25 04:05:11

99

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A function with a point of slope of exactly $2$

Published on 25 Dec 2019 - 4:05

score 558 · Answer 2 · 2019-12-27 22:15:56

558

Views

Non negative derivative, not being zero function on all subintervals, implies strictly increasing

Published on 27 Dec 2019 - 22:15

score 133 · Answer 3 · 2020-01-15 16:07:46

133

Views

Rolle's theorem with odd function

Published on 15 Jan 2020 - 16:07

score 38 · Answer 4 · 2020-01-18 17:31:57

38

Views

Prove that $f(a)=\ell + \frac{(a-\ell)^{2}}{2}f''(c)$

Published on 18 Jan 2020 - 17:31

score 607 · Answer 5 · 2020-01-27 16:37:56

607

Views

Using Rolle’s Theorem prove that the cubic equation $x^3+ax+b$ has at most one root

Published on 27 Jan 2020 - 16:37

score 137 · Answer 6 · 2020-02-12 06:23:43

137

Views

$f:\Bbb{R}\mapsto\Bbb{R}$ and $f$ is twice differentiable.

Published on 12 Feb 2020 - 6:23

score 43 · Answer 7 · 2020-02-13 01:45:45

43

Views

Mean value theorem and the continuity of step length

Published on 13 Feb 2020 - 1:45

score 379 · Answer 8 · 2020-02-14 22:02:33

379

Views

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

Published on 14 Feb 2020 - 22:02

score 160 · Answer 9 · 2020-02-16 17:19:54

160

Views

Show that the polynomial $f(x) = 3x^4 - 2 x^3 + x^2 + ax - 1$ with $a \in \mathbb{R}$ does not have all of its roots real.

Published on 16 Feb 2020 - 17:19

score 89 · Answer 10 · 2020-02-25 11:53:00

89

Views

Prove that there exists some $\xi\in(-\frac{\pi}{2},\frac{\pi}{2})$ such that $f''(\xi)=f(\xi)(1+2\tan^{2}{\xi}).$

Published on 25 Feb 2020 - 11:53

score 68 · Answer 11 · 2020-02-26 14:09:52

68

Views

Prove that $\nexists c \in ]-1,1[$ such that $f'(c) = 0$

Published on 26 Feb 2020 - 14:09

score 72 · Answer 12 · 2020-03-03 15:42:23

72

Views

Use Rolle to determine the number of possible solution of $f(x) = \sin x + x + 1$

Published on 03 Mar 2020 - 15:42

score 125 · Answer 13 · 2020-03-16 04:16:49

125

Views

Prove that there exists a line passing through M$(\alpha,\beta)$ which is tangent to the graph of $f$.

Published on 16 Mar 2020 - 4:16

score 95 · Answer 14 · 2020-03-17 05:30:06

95

Views

Does Rolle's theorem apply for roots at infinity?

Published on 17 Mar 2020 - 5:30

score 99 · Answer 15 · 2020-03-22 17:38:06

99

Views

Question on Rolle's Theorem

Published on 22 Mar 2020 - 17:38

List Question

A function with a point of slope of exactly $2$

Non negative derivative, not being zero function on all subintervals, implies strictly increasing

Rolle's theorem with odd function

Prove that $f(a)=\ell + \frac{(a-\ell)^{2}}{2}f''(c)$

Using Rolle’s Theorem prove that the cubic equation $x^3+ax+b$ has at most one root

$f:\Bbb{R}\mapsto\Bbb{R}$ and $f$ is twice differentiable.

Mean value theorem and the continuity of step length

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

Show that the polynomial $f(x) = 3x^4 - 2 x^3 + x^2 + ax - 1$ with $a \in \mathbb{R}$ does not have all of its roots real.

Prove that there exists some $\xi\in(-\frac{\pi}{2},\frac{\pi}{2})$ such that $f''(\xi)=f(\xi)(1+2\tan^{2}{\xi}).$

Prove that $\nexists c \in ]-1,1[$ such that $f'(c) = 0$

Use Rolle to determine the number of possible solution of $f(x) = \sin x + x + 1$

Prove that there exists a line passing through M$(\alpha,\beta)$ which is tangent to the graph of $f$.

Does Rolle's theorem apply for roots at infinity?

Question on Rolle's Theorem

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