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What is Lagrange’s Mean Value theorem?
What is Lagrange’s Mean Value theorem? Explain with examples
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Mean Value Theorem (MVT)
The Lagrange value theorem (MVT) states that if the work continues in a closed space and is separated from the open space then there is at least one point at this time.
This theorem (also known as the First Mean Value Theorem) allows to express the increase in activity in space by the derivative value in the center part of the part.
Rolle’s Theorem is a specific set of theorem of the fair value that satisfies certain conditions. At the same time, Lagrange’s mean value theorem is a value that means the actual value or the first theorem of the mean value. Generally, one can understand that it means the average of a given number. But in the case of integration, the process of finding the mean value of two different functions is different. Let’s read Rolle’s theorem and the mean number of such functions and their geometric descriptions.
Lagrange Mean Value Theorem
If task f is defined in the closed period [a, b] to satisfy the following conditions –
i) Activity f continues in a closed space [a, b]
ii) Work f is separated from the open space (a, b)
Then there is the value x = c in the sense that
f ‘(c) = [f (b) – f (a)] / (b-a)
This theorem is also known as the first theorem of mean value or theorem of the value meaning Lagrange.
