Class 12 | Ch-5 | Pt-3 | Differentiability| Rolle's and Lagrange's Theorem | IMPORTANT Questions

0:00 - Introduction to Rolle's Theorem and Lagrange's Mean Value Theorem
0:30 - Conditions for Rolle's Theorem
3:08 - Graphical Representation of Rolle's Theorem
6:17 - Understanding Slope and Tangents
7:23 - Multiple Points in Rolle's Theorem
8:47 - Applicability of Rolle's Theorem
9:08 - Introduction to Lagrange's Mean Value Theorem
10:01 - Conditions for Lagrange's Mean Value Theorem
11:23 - Graphical Representation of Lagrange's Mean Value Theorem
13:12 - Comparing Rolle's and Lagrange's Theorems
15:20 - Problem Solving - Proving dy/dx for a given equation
19:39 - Problem Solving - Proving a quantity is constant for a circle equation
25:24 - Problem Solving - Proving dy/dx for a trigonometric equation
27:25 - Problem Solving - Deriving Cosine Sum Formula using Differentiation
30:57 - Problem Solving - Second Order Derivative of y = e^(a cos⁻¹x)
36:37 - Properties and Continuity of Modulus Function (|x|)
41:33 - Differentiability of Modulus Function (|x|)
47:00 - Solving f(x) = |x|³ Problem

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