27.Lagrange’s Mean Value Theorem | Geometrical Interpretation & Solved Examples | M1 Unit-III

In this video, we explain Lagrange’s Mean Value Theorem (LMVT) with Geometrical Interpretation and solved examples. This theorem is one of the most important topics in Engineering Mathematics – M1 (Unit III, JNTUH R22 syllabus) and frequently appears in semester exams.

📌 In this video, you will learn:

✅ Statement and conditions of Lagrange’s Mean Value Theorem
✅ Geometrical meaning and graphical explanation
✅ Step-by-step working rule to verify LMVT
✅ Solved examples for better understanding
✅ Difference between Rolle’s Theorem and LMVT
✅ Applications and exam tips

💡 Why this topic is important:
Lagrange’s Mean Value Theorem is the foundation for Cauchy’s Mean Value Theorem and plays an essential role in differential calculus and analysis. It helps in understanding how derivatives describe the behavior of real-world functions and is crucial for both academic and competitive exams.

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Stay tuned for the next video, where we’ll discuss Cauchy’s Mean Value Theorem and Taylor’s Series Expansion with examples.