List questions from mean-value-theorem

Published on 23 Feb 2026 - 13:25

207

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An identity $ \int_{\partial B(0,1)}u(x_0+aw)u(x_0+cw)$ with a harmonic function $u$

Published on 23 Feb 2026 - 13:26

952

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If $f$ is twice differentiable and satisfies the following constraints, prove that $f'(0)\geq-\sqrt 2$.

Published on 23 Feb 2026 - 13:30

192

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Show that there exist $\gamma\in[\alpha,\beta] $ such that $\int\limits_{E}f|g|=\gamma\int\limits_{E}|g|$

Published on 23 Feb 2026 - 13:28

136

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Showing that $\sup_{x\in[0,1]}|f(x)|\leq \sqrt{\int_0^1(f'(x))^2dx}$ when $f\in C^1([0,1],\mathbb{R})$ and $f(0) = 0$

Published on 23 Feb 2026 - 13:30

149

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Application of Mean Value Theorem to a function from $\mathbb{R}^3$ to $\mathbb{R}$

Published on 23 Feb 2026 - 13:26

108

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An add-on question on Rolle's theorem

Published on 23 Feb 2026 - 13:26

334

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Why do we need continuity at the end points of the interval for Rolle's theorem?

Published on 23 Feb 2026 - 13:28

159

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Proving an integral identity for a continuous function

Published on 23 Feb 2026 - 13:23

49

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Proving uniform convergence using MVT for definite integrals

Published on 23 Feb 2026 - 13:24

183

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If $f:[0,1] \to \mathbb{R}$ is of bounded variation, is $|f'|$ is integrable?

Published on 23 Feb 2026 - 13:03

149

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Prove the inequality with the mean value/Lagrange theorem

Published on 23 Feb 2026 - 13:25

92

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Prove by Mean Value Theorem $\ln(1+x) \ge\frac{x}{1+x}$ for $x>-1$

Published on 23 Feb 2026 - 13:30

42

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Does the HM follow the same pattern as AM and GM of the particular MVT application/theorem?

Published on 23 Feb 2026 - 13:29

69

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Estimate value of harmonic function in the annulus

Published on 23 Feb 2026 - 13:24

List Question

Converse of mean value theorem

An identity $ \int_{\partial B(0,1)}u(x_0+aw)u(x_0+cw)$ with a harmonic function $u$

If $f$ is twice differentiable and satisfies the following constraints, prove that $f'(0)\geq-\sqrt 2$.

Show that there exist $\gamma\in[\alpha,\beta] $ such that $\int\limits_{E}f|g|=\gamma\int\limits_{E}|g|$

Showing that $\sup_{x\in[0,1]}|f(x)|\leq \sqrt{\int_0^1(f'(x))^2dx}$ when $f\in C^1([0,1],\mathbb{R})$ and $f(0) = 0$

Application of Mean Value Theorem to a function from $\mathbb{R}^3$ to $\mathbb{R}$

An add-on question on Rolle's theorem

Why do we need continuity at the end points of the interval for Rolle's theorem?

Proving an integral identity for a continuous function

Proving uniform convergence using MVT for definite integrals

If $f:[0,1] \to \mathbb{R}$ is of bounded variation, is $|f'|$ is integrable?

Prove the inequality with the mean value/Lagrange theorem

Prove by Mean Value Theorem $\ln(1+x) \ge\frac{x}{1+x}$ for $x>-1$

Does the HM follow the same pattern as AM and GM of the particular MVT application/theorem?

Estimate value of harmonic function in the annulus

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