Find the Minimum Value of f(x,y) = x² + y² + 6x + 12 | Maxima & Minima | Example 1 | Calculus |

In this video, we solve a classic Maxima and Minima problem for functions of two variables: f(x,y) = x² + y² + 6x + 12. We walk through the full method step by step: ✅ Finding first-order partial derivatives (fx, fy) ✅ Solving for the stationary point ✅ Computing second-order partials (A, B, C) ✅ Applying the AC − B² test to classify the point ✅ Calculating the minimum value of the function This is a common exam-style question (JAN-22-R-21) and a great example for anyone learning multivariable calculus, engineering mathematics, or preparing for board / competitive exams. 📌 Topics covered: Partial derivatives Stationary points Second derivative test for functions of two variables Classifying maxima, minima, and saddle points ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 RESOURCES & LINKS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📥 Download PDF Notes :https://engineeringmathematica.blogsp... 📲 WhatsApp Channel — Latest Updates & Tips: https://whatsapp.com/channel/0029VaAU... 💬 WhatsApp Direct — Got Questions? Message Me: https://wa.me/message/HM5KUVTAFENSA1 📢 Telegram — Download Study Materials: https://t.me/engineerinmathematica 🧠 Full Course Playlist — MA25C01-UNIT II:    • MA25C01-UNIT II - FUNCTION OF SEVERAL VARI...   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 PERFECT FOR STUDENTS STUDYING ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 MA25C01 — Applied Calculus (Anna University & Affiliates) 🎓 Calculus 1 / Engineering Mathematics 🎓 Limits & Continuity Chapter 🎓 B.E. / B.Tech First Year Mathematics 👍 If this helped, like, comment, and subscribe for more step-by-step math tutorials! #Calculus #MaximaAndMinima #PartialDerivatives #EngineeringMathematics #MathTutorial