Скачать или смотреть Maxima and minima engineering mathematics | Extreme Values | Part 2

🎓 Maxima and Minima | Find Extreme Values of f(x, y) = x³ + 3xy² − 15x² − 15y³ + 72x | VTU Calculus & Linear Algebra
In this video, we solve an important Maxima and Minima problem from functions of two variables, a key topic under Partial Differentiation in Calculus & Linear Algebra for VTU 1st Semester B.E. Students.

📘 Question:
Find the maximum and minimum values of the function
f(x, y) = x³ + 3xy² − 15x² − 15y³ + 72x
We determine the first-order partial derivatives, find the stationary (critical) points, and apply the second derivative test to classify each point as a maximum, minimum, or saddle point.

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 Detailed Explanation


🎯 Perfect For:
VTU Exam Preparation, Internal Tests, and Assignments

📘 *Questions Covered in This Playlist*

🟦 *Part 1*
Find the extreme values of the function:
f(x, y) = x³ + y³ − 3x − 12y + 20
🔗    • Maxima and minima engineering mathematics ...  

🟦 *Part 2*
Find the maximum and minimum values of the function:
f(x, y) = x³ + 3xy² − 15x² − 15y³ + 72x
🔗    • Maxima and minima engineering mathematics ...  

🟦 *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 ...  

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📚 *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

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🎯 *Ideal For:*
✔ VTU B.E. 1st Semester Students
✔ VTU Exam Preparation
✔ Internal Assessments
✔ Assignment Practice
✔ Quick Concept Revision


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