VTUM1|Maxima and Minima for Functions of Two Variables Introduction and problems

📘 Finding Maxima and Minima for Functions of Two Variables | Engineering Mathematics 1

🎯 Master the crucial concept of maxima and minima for functions of two variables, a vital part of your Engineering Mathematics–1 syllabus!

👉 Example discussed:
find the extreme values of the function f(x,y)=x^3+y^3-3x-12y+20.Maxima & Minima for Functions of Two Variables

In this video, we’ll dive deep into finding the extreme values (maxima and minima) of multivariable functions, equipping you with the skills to solve a variety of questions asked in exams.

💡 VTU Note: The questions from this chapter are not very difficult but carry good weightage. Mastering this topic will help you secure full marks. So keep your pen and notebook ready, and practice along with me. Don’t skip any part — every step matters!

📚 What You’ll Learn:

🔹 Understanding Maxima and Minima

Local vs. global maxima/minima 🌄

Difference between single-variable and two-variable extrema

🔹 The Second Derivative Test

How to classify stationary points using second-order partial derivatives ✍️

Discriminant condition: D = fxx .fyy - (fxy)^2

🔹 Finding Critical Points

Step-by-step process of setting ∂f/∂x = 0 and ∂f/∂y = 0

🔹 Applying the Second Derivative Test

Compute A = fxx, B = fxy, C = fyy

Use D = AC - B^2 to decide:
✅ If D greater 0 and A greater 0 → Local Minimum
✅ If D greater 0 and A lesser 0 → Local Maximum
✅ If D greater 0 → Saddle Point
✅ If D = 0 → Inconclusive

🔹 Real-world Applications

Optimizing designs
Minimizing costs
Maximizing efficiency
Machine learning algorithms

🌟 Why This Video is for You:
✨ Essential for Engineering Mathematics–1 success
✨ Clear and concise explanations of complex concepts
✨ Practical examples to boost your confidence
✨ Problem-solving skills for optimization challenges

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📌 Playlists:

▶️ Engineering Mathematics 1 Playlist
   • VTU Engineering Maths 2 2022/21/17/18 scheme  

▶️ Engineering Mathematics 2 Playlist
   • VTU Engineering Maths 1 2022/21/17/18 scheme  

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