Maxima and Minima Class 12

Maxima and Minima Made Easy! For Live Classes, Concept Videos, Quizzes, Mock Tests & Revision Notes please see our Website/App: Our Website: http://bit.ly/2KBC0l1 Android App: https://bit.ly/3k48zdK CBSE Class 12 Courses: https://bit.ly/4h0L7IN CBSE Class 11 Courses: https://bit.ly/48isN9Q CBSE Class 10 Courses: https://bit.ly/363U55V CBSE Class 9 Courses: https://bit.ly/39Pm7mM CBSE Class 8 Courses: https://bit.ly/3bJByzB ICSE Class 10 Courses: https://bit.ly/2MaXpFo ICSE Class 9 Courses: https://bit.ly/3iFV7dl ICSE Class 8 Courses: https://bit.ly/3boM5OB IGCSE Courses: https://bit.ly/2YNwQcn Artificial Intelligence: https://bit.ly/3vm3FAE Python Coding: https://bit.ly/3nX0s2y Java Coding: https://bit.ly/3chHTAK Facebook page: http://bit.ly/2s6VYhf In mathematics, maxima and minima are points where a function reaches its highest or lowest value, either in a small neighborhood or over its entire domain. 1. Maximum (Maxima) * A maximum is a point where the function has the greatest value compared to nearby points. * Local or relative maximum: The function is larger at that point than at nearby values. * Global or absolute maximum: The function is larger at that point than at all other values in the domain. 2. Minimum (Minima) * A minimum is a point where the function has the least value compared to nearby points. * Local or relative minimum: The function is smaller at that point than at nearby values. * Global or absolute minimum: The function is smaller at that point than at all other values in the domain. 3. How to find maxima and minima: For a differentiable function f(x): * Find the critical points where f′(x) = 0 or f′(x) is undefined. * Use the second derivative test: * If f′′(x) is greater than 0, the point is a local minimum. * If f′′(x) is less than 0, the point is a local maximum. * If f′′(x) = 0, the test is inconclusive. At Manocha Academy, learning Science and Math is Easy! The school coursework is explained with simple examples that you experience every day! Yes, Science & Math is all around you! Let's learn every day from everyday life!