query: Using the mean value theorem to solve an inequality
positive_passages.docid: 16418
positive_passages.text: Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 1305
negative_passages.text: Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
negative_passages.docid: 106815
negative_passages.text: Better bound for integral inequality
negative_passages.docid: 48920
negative_passages.text: Mean value theorem for integrals: how does the sign matter?
negative_passages.docid: 48476
negative_passages.text: Mean value theorem rolle's theorem
negative_passages.docid: 106316
negative_passages.text: Finding a bound on the maximum of the absolute value of normal random variables
negative_passages.docid: 77645
negative_passages.text: Generalized mean value theorem
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality
negative_passages.docid: 35867
negative_passages.text: Squaring sides of an inequality
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 157432
negative_passages.text: How to use the Mean Value Theorem to prove the following statement:
negative_passages.docid: 52999
negative_passages.text: Convergence in quadratic mean and in mean
negative_passages.docid: 78599
negative_passages.text: 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?
negative_passages.docid: 51546
negative_passages.text: Geometrical Interpertation of Cauchy's Mean Value Theorem
negative_passages.docid: 19845
negative_passages.text: Mean Value Theorem for Integrals
negative_passages.docid: 24617
negative_passages.text: Proof of Inequality using AM-GM