Question

Does there exists a continuous function $f(x)$ such that $f(0)=10,f(2)=2, f'(x) \le 1,\forall x\in (0,2)?$

score 1.3k · Answer 1 · 2022-03-12 01:09:33

1.3k

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Does there exists a continuous function $f(x)$ such that $f(0)=10,f(2)=2, f'(x) \le 1,\forall x\in (0,2)?$

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List Question

Does there exists a continuous function $f(x)$ such that $f(0)=10,f(2)=2, f'(x) \le 1,\forall x\in (0,2)?$

Error of Simpson's Rule

Proof for Mean value theorem for integrals

Proving an inequality(with a term in cosine) using the mean value theorem

Mean value theorem related question

Suppose that $f$ is differentiable on $\mathbb{R}$, that $f(1)=1$ and $f(7)=5$. Show that there exists $c\in(0,4)$ such that $f'(c)=\frac{2}{3}$.

Mean Value Theorem question (show that f is constant)

DIfferentiable function and generalized mean value theorem

Mean Value function theorem on a Riemannian Manifold

A Counterexample to the Mean Value Theorem for Integrals (Complex Case)

Showing the existence of a zero value at some point in the below functions

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Why is it important that we use the Mean value theorem on an interval?

Mean Value Theorem Question on intervals

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