Finding maxima and Minima Using Second Derivative Test (with Example)

# Finding maxima and Minima Using Second Derivative Test (with Example) Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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

 1. What is the second derivative test for finding maxima and minima?
The second derivative test is a method used to determine whether a critical point of a function corresponds to a maximum, minimum, or neither. It involves evaluating the second derivative at the critical point. If the second derivative is positive, the critical point corresponds to a local minimum. If the second derivative is negative, the critical point corresponds to a local maximum. If the second derivative is zero, the test is inconclusive and further analysis is needed.
 2. How can the second derivative test be applied to find maxima and minima?
To apply the second derivative test, follow these steps: 1. Find the critical points of the function by setting its first derivative equal to zero. 2. Evaluate the second derivative of the function at each critical point. 3. If the second derivative is positive at a critical point, it corresponds to a local minimum. 4. If the second derivative is negative at a critical point, it corresponds to a local maximum. 5. If the second derivative is zero at a critical point, the test is inconclusive, and further analysis is needed using other methods.
 3. Can the second derivative test be used to find absolute maxima and minima?
No, the second derivative test can only determine whether a critical point corresponds to a local maximum or minimum. It does not provide information about absolute maxima or minima. To find absolute maxima and minima, other methods such as the first derivative test or evaluating endpoints of a closed interval need to be used.
 4. What should be done if the second derivative is zero at a critical point?
If the second derivative is zero at a critical point, the second derivative test is inconclusive. In such cases, further analysis is needed. One possible method is to use the first derivative test. By examining the sign changes of the first derivative around the critical point, it is possible to determine whether it corresponds to a maximum, minimum, or neither.
 5. Are there any limitations or conditions for applying the second derivative test?
Yes, there are some limitations and conditions for applying the second derivative test. The function must be twice differentiable, meaning that its first and second derivatives exist and are continuous. Additionally, the critical points must be isolated, meaning that there are no other critical points nearby. If these conditions are not met, the second derivative test may not provide accurate results, and alternative methods should be used for finding maxima and minima.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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