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Maximum and Minimum Value of a Function in a Closed Interval Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Maximum and Minimum Value of a Function in a Closed Interval Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the definition of a closed interval in mathematics?
Ans. In mathematics, a closed interval is a set of real numbers that includes both its endpoints. It is denoted by [a, b], where a and b are the endpoints of the interval.
2. How do you find the maximum value of a function in a closed interval?
Ans. To find the maximum value of a function in a closed interval, you need to evaluate the function at the critical points within the interval and at the endpoints. The largest value obtained from these evaluations will be the maximum value of the function in the closed interval.
3. How do you find the minimum value of a function in a closed interval?
Ans. To find the minimum value of a function in a closed interval, you need to evaluate the function at the critical points within the interval and at the endpoints. The smallest value obtained from these evaluations will be the minimum value of the function in the closed interval.
4. Can a function have multiple maximum or minimum values in a closed interval?
Ans. Yes, it is possible for a function to have multiple maximum or minimum values in a closed interval. This can occur when the function has multiple critical points within the interval or if the function is not continuous.
5. How can calculus help in finding the maximum and minimum values of a function in a closed interval?
Ans. Calculus provides a systematic approach to finding the maximum and minimum values of a function in a closed interval. By taking the derivative of the function and analyzing its critical points, we can determine where the function reaches its extreme values. Additionally, by evaluating the function at the endpoints of the closed interval, we can identify any potential maximum or minimum values.
204 videos|288 docs|139 tests

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