Partial Differentiation | Find Extreme Values of f(x,y)=sinx+siny+sin(x+y) | Multivariable Calculus
Автор: Mathematics Tutor
Загружено: 2025-01-23
Просмотров: 7520
📘 Calculus & Multivariable Calculus | Partial Differentiation & Extremum Problems | Problem Solution
📝 Problem Statement:
Find the *extreme values* of the function
*f(x, y) = sin x + sin y + sin(x + y).*
🎯 Concepts Used:
✔️ Partial Differentiation (∂f/∂x and ∂f/∂y to find critical points)
✔️ Solve simultaneous trigonometric equations to locate stationary points
✔️ Second Derivative Test / Hessian Determinant to classify extrema
✔️ Identification of maxima, minima, or saddle points using trigonometric identities
✨ This problem illustrates how to find and classify stationary points of a trigonometric function of two variables using partial derivatives and the Hessian determinant. Such problems are common in *VTU exams* and engineering mathematics for optimization of multivariable trigonometric expressions.
✅ Very useful for Engineering Mathematics, Multivariable Calculus, Trigonometric Optimization, and VTU exam preparation.
#Calculus #PartialDifferentiation #MultivariableCalculus #Extrema #TrigonometricFunctions #Optimization #VTU #EngineeringMathematics #BMATS201 #BMATE201 #BMATC201 #BMATM201 #1BMATS101 #1BMATE101 #1BMATC101 #1BMATM101 #Module1 #Module2
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