# Questions tagged [extreme-value-theorem]

This tag is for questions relating to "Extreme Value Theorem". The Extreme Value Theorem guarantees both a maximum and minimum value for a function under certain conditions.

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### Stationary points problem

I already made a first derivation of $f\left ( s,t \right )$. For $\frac{\partial f}{\partial s}=4s^{3}-2s-2t$ and for $\frac{\partial f}{\partial t}=4t^{3}-2s-2t$. I have to find the stationary ...
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### Local extreme of function : $f\left ( x,y \right) =x^{2}+2x+y^{2}-2y+3$ [closed]

I am supposed to find the local extreme of function : $f\left ( x,y \right) =x^{2}+2x+y^{2}-2y+3$ on circle with the origin in the coordinate axis and radius $2\sqrt{2}$. I know how should I do this, ...
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### What is the maximum possible value for $f(x)$ for $x \in [0,1]$? [closed]

A function $f(x)$ is continuous and differentiable in $[0,1]$. If $f'(x) \le 10$ for all $x \in [0, 1]$ and $f(0) = 0$, what is the maximum possible value of $f(x)$ for $x$ in $[0, 1]$?
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### Trouble understanding how the Transfer Principle is applied for the Extreme Value theorem.

I am reading Keisler's Elementary Calculus (which can be downloaded here). I am having trouble understanding his proof sketch of Extreme Value Theorem and how he is applying the Transfer Principle. ...
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### Proving and disproving some statements based on Extreme Value Theorem

Here are the statements: Suppose that $f$ is continuous on the interval $[a,b)$ and that $\lim_{x\to b^{-}} f(x) = +\infty$. Then $f(a) \le f(x)$ for all $x$ in $[a,b)$. Suppose that $f$ is ...