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Differential Calculus | LMVT Video Lecture | Crash Course for UGC NET Economics

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FAQs on Differential Calculus - LMVT Video Lecture - Crash Course for UGC NET Economics

1. What is the Mean Value Theorem in differential calculus?
Ans. The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the instantaneous rate of change (derivative) equals the average rate of change of the function over the interval [a, b].
2. How is the Mean Value Theorem used in calculus problems?
Ans. The Mean Value Theorem is often used to prove the existence of certain values or points in a function. It can also be used to approximate values of a function or determine when a function reaches a certain value based on its rate of change.
3. Can the Mean Value Theorem be applied to all functions?
Ans. No, the Mean Value Theorem can only be applied to functions that satisfy the conditions of being continuous on a closed interval and differentiable on an open interval. Functions that do not meet these criteria cannot have the Mean Value Theorem applied to them.
4. How does the Mean Value Theorem relate to finding local extrema of a function?
Ans. The Mean Value Theorem can be used to prove the existence of local extrema (maximum or minimum points) in a function. If the derivative of a function is zero at a certain point, the Mean Value Theorem can show that there must be a local extremum at that point.
5. What is the significance of the Mean Value Theorem in real-world applications?
Ans. The Mean Value Theorem is crucial in various real-world applications, such as in physics, engineering, and economics, where it helps in analyzing rates of change, determining critical points, and making predictions based on the behavior of functions.
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