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Examples : Absolute maxima and minima Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Examples : Absolute maxima and minima Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the definition of absolute maxima and minima?
Ans. Absolute maxima and minima refer to the highest and lowest values that a function can achieve within a given interval or on its entire domain. These points represent the extreme values of the function.
2. How can I find the absolute maximum and minimum of a function?
Ans. To find the absolute maximum and minimum of a function, you need to analyze the critical points (where the derivative is zero or undefined) and the endpoints of the given interval. By evaluating the function at these points, you can determine the absolute maximum and minimum values.
3. Is it possible for a function to have multiple absolute maxima or minima?
Ans. Yes, a function can have multiple absolute maxima or minima if it reaches the same extreme value at different points within the interval. This can occur when the function has flat regions or multiple peaks and valleys.
4. What is the difference between absolute maxima/minima and local maxima/minima?
Ans. Absolute maxima and minima are the global extreme values of a function, representing the highest and lowest points over the entire interval or domain. On the other hand, local maxima and minima refer to the highest and lowest points within a specific region of the function, often around critical points.
5. Can a function have an absolute maximum or minimum if it is not continuous?
Ans. No, a function must be continuous over the given interval to have an absolute maximum or minimum. If a function is not continuous, it may have local maxima or minima, but it cannot have absolute extreme values. Continuity ensures that there are no gaps or jumps in the function's graph.
204 videos|288 docs|139 tests

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