Maxima, Minima and Saddle Points IN 3 STEPS (Function of 2 variables)
Optimization exercise. Calculate the local maxima, local minima, and saddle points of a function of two variables using partial derivatives, critical points, and the determinant of the Hessian matrix, step by step.
Full Course: • Curso Completo de Cálculo de varias variab...
00:00 - Introduction and presentation of the exercise
00:10 - STEP 1: Calculation of first-order partial derivatives
00:54 - Solving the system of equations to find critical points
02:12 - Identification of the 4 critical points
03:14 - STEP 2: Calculation of second-order partial derivatives
04:15 - STEP 3: Classification using the determinant of the Hessian matrix
04:51 - Evaluation of the first point (0,0): Saddle Point
06:22 - Evaluation of the second point (0,2): Local Minimum
07:00 - Evaluation of the third point (-2,0): Local Maximum
07:34 - Evaluation of the fourth point (-2,2): Point Chair
08:08 - Conclusion and Acknowledgments
#derivatives #functions #mathematics
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** BIBLIOGRAPHY **
Calculus of Several Variables, by James Stewart
Vector Calculus, by Marsden and Tromba
Multivariable Calculus, by Ron Larson
Multivariable Calculus, by Thomas
Vector Calculus, by Claudio Pita Ruiz
Multivariable Calculus, by Juan de Burgos
Calculus II, by Tom M. Apóstol
Early Transcendental Calculus, by Anton
Advanced Calculus, by Fulks
Advanced Calculus, by Kaplan
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