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Finding maxima and minima Using First Derivative Test (with Example) Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Finding maxima and minima Using First Derivative Test (with Example) Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the First Derivative Test for finding maxima and minima?
Ans. The First Derivative Test is a method used to find the maximum and minimum points of a function. It involves analyzing the sign of the derivative of the function at critical points. If the derivative changes from positive to negative at a critical point, it indicates a local maximum. Conversely, if the derivative changes from negative to positive, it indicates a local minimum.
2. How do you determine critical points in a function?
Ans. Critical points in a function are the points where the derivative is either zero or undefined. To find these points, we set the derivative of the function equal to zero and solve the resulting equation. The solutions obtained are the critical points. Additionally, if the derivative is undefined at any point, that point is also considered a critical point.
3. Can a function have multiple local maxima or minima points?
Ans. Yes, a function can have multiple local maxima and minima points. This occurs when the derivative changes sign multiple times within a given interval. Each sign change indicates a transition from a maximum to a minimum or vice versa. Therefore, if a function has multiple critical points and the derivative changes sign at each point, there will be multiple local maxima and minima.
4. Are all critical points of a function local maxima or minima?
Ans. No, not all critical points of a function are local maxima or minima. Critical points can also be inflection points or points of discontinuity. Inflection points occur when the concavity of the function changes, and they do not correspond to maxima or minima. Points of discontinuity can be vertical asymptotes or holes in the graph, and they are not associated with maxima or minima either.
5. How can the First Derivative Test be used to identify global maxima and minima?
Ans. The First Derivative Test can only identify local maxima and minima. To determine if a critical point is a global maximum or minimum, further analysis is required. This can be done by evaluating the function at the critical points as well as at the endpoints of the interval under consideration. The highest and lowest values obtained from this evaluation will correspond to the global maximum and minimum points of the function, respectively.
204 videos|288 docs|139 tests

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