Interesting application of mean value theorem
118266
If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
26250
Robust mean estimation with O(1) update efficiency
4064
An equality involving the mean value property
19845
Mean Value Theorem for Integrals
140871
Different Applications of Sylow Theorems
67738
Mean Value theorem problem?(inequality)
151936
Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
129765
Mean value theorem for the second derivative, when the first derivative is zero at endpoints
45342
Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
17159
Proof of Closest Point Theorem in Hilbert Space
140516
How does one prove the Taylor's Theorem by the Cauchy's Mean Value Theorem?
22067
Generalisation of Dominated Convergence Theorem
146519
gaussian and mean curvatures
78599
How to prove that $\frac{b-a}{\sqrt{1-a^2}}<\sin^{-1}b-\sin^{-1}a<\frac{b-a}{\sqrt{1-b^2}}$ by using Mean Value Theorem?
48476
Mean value theorem rolle's theorem
58041
Prove by Mean Value Theorem $\frac{x}{1+x}0$