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An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
- Supremum or Infimum
The infimum and supremum are concepts in mathematical...
- Second Derivative Test
The second derivative test is used to determine if a given...
- Optimization
An extremum is a maximum or minimum value of a function, in...
- Critical Points
A local extremum is a maximum or minimum of the function in...
- Function
Functions can possess some degree of symmetry.A function is...
- Supremum or Infimum
In mathematical analysis, the maximum and minimum[a] of a function are, respectively, the greatest and least value taken by the function.
When we are trying to find the absolute extrema of a function on an open interval, we cannot use the Extreme Value Theorem. However, if the function is continuous on the interval, many of the same ideas apply. In particular, if an absolute extremum exists, it must also be a relative extremum.
10 paź 2019 · In many cases, extrema look like the crest of a hill or the bottom of a bowl on a graph of the function. A global extremum is always a local extremum too, because it is the largest or smallest value on the entire range of the function, and therefore also its vicinity.
17 lis 2020 · If \(f(x_0,y_0)\) is either a local maximum or local minimum value, then it is called a local extremum (see the following figure). Figure \(\PageIndex{2}\) : The graph of \(z=\sqrt{16−x^2−y^2}\) has a maximum value when \((x,y)=(0,0)\).
A function \(f\) has a local extremum at \(c\) if \(f\) has a local maximum at \(c\) or \(f\) has a local minimum at \(c\). Note that if \(f\) has an absolute extremum at \(c\) and \(f\) is defined over an interval containing \(c\), then \(f(c)\) is also considered a local extremum.
An extremum (plural: extrema) is a maximum (plural: maxima) or a minimum. Let $f$ be a function on $I\subset\mathbb{R}$ and let $x_0\in\ I$. We say that $f$ have a local maximum (resp. local minimum) at $x_0$ if $f(x)<f(x_0)$ (resp. $f(x)>f(x_0)$) in the strict neighborhood of $x_0$ (i.e. $|x-x_0|<\epsilon$ for some $\epsilon>0$ and $x\not=x_0$).
