Find Extreme Values of f(x, y) = x³ + y³ − 3x − 12y + 20 | Engineering Mathematics

🎓 Maxima and Minima | Find Extreme Values of f(x, y) = x³ + y³ − 3x − 12y + 20 | VTU Calculus & Linear Algebra In this video, we solve an important problem on Maxima and Minima of functions of two variables, a key topic from Partial Differentiation in Calculus & Linear Algebra for VTU 1st Semester B.E. Students. 📘 Question: Find the extreme values of the function f(x, y) = x³ + y³ − 3x − 12y + 20 We find the first and second order partial derivatives, locate the critical points, and use the second derivative test to determine whether the points are maxima, minima, or saddle points. This topic is part of: 🔹 1BMATS101 – Calculus and Linear Algebra 🔹 1BMATE101 – Differential Calculus & Linear Algebra 🔹 1BMATC101 – Differential Calculus and Linear Algebra 🔹 1BMATM101 – Differential Calculus and Linear Algebra 📚 Concepts Covered: Partial Derivatives and stationary points Second Derivative Test for two variables Finding Maxima and Minima Step-by-step solution with complete explanation Perfect for 🎯 VTU exam preparation, internal tests, and assignments. 🟦 *Part 1* Find the extreme values of the function: f(x, y) = x³ + y³ − 3x − 12y + 20 🔗    • Find Extreme Values of f(x, y) = x³ + y³ −...   🟦 *Part 2* Find the maximum and minimum values of the function: f(x, y) = x³ + 3xy² − 15x² − 15y³ + 72x 🔗    • Find Maxima and Minima | x³ + 3xy² − 15x² ...   🟦 *Part 3* Examine the function for extreme values: f(x, y) = xy(a − x − y) 🔗    • Maxima and minima engineering mathematics ...   🟦 *Part 4* Find the extreme values of the function: f(x, y) = x³y²(1 − x − y) 🔗    • Maxima and minima engineering mathematics ...   --- 📚 *This Playlist Covers Concepts From:* 🔹 1BMATS101 – Calculus and Linear Algebra 🔹 1BMATE101 – Differential Calculus & Linear Algebra 🔹 1BMATC101 – Differential Calculus and Linear Algebra 🔹 1BMATM101 – Differential Calculus and Linear Algebra 📘 *Topics Included:* Partial Derivatives Stationary Points Second Derivative (Hessian) Test Maxima, Minima & Saddle Points Exam-focused problem solving Parameter-dependent extreme value problems --- 🎯 *Ideal For:* ✔ VTU B.E. 1st Semester Students ✔ VTU Exam Preparation ✔ Internal Assessments ✔ Assignment Practice ✔ Quick Concept Revision --- 💎 *Support Us* Join our channel and get access to exclusive perks 👇 🔗    / @officialmathematicstutor   --- 💎 Support Us: Join our channel and get access to exclusive perks 👇 🔗    / @officialmathematicstutor   #MaximaAndMinima #PartialDifferentiation #VTUMathematics #VTU #CalculusAndLinearAlgebra #VTU1stSem #EngineeringMathematics #DifferentialCalculus #MathsMadeSimple #VTUBEMS #VTUExamPreparation #BMATS101 #BMATE101 #BMATC101 #BMATM101 #VTUMaths