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How to Prove $f(x)$ is Constant using Lagrange Mean Value Theorem | LMVT Applications: Proving Constant Functions & $f'(x) = g'(x)$ | Calculus Craze | Calculus-1: Mean Value Theorem Proofs & Applications | Abdul Fatah Khalil Rajri

Master the Practical Applications of the Lagrange Mean Value Theorem (LMVT)!

In this session of Calculus-1 and Real Analysis, Instructor Abdul Fatah Khalil Rajri demonstrates how to use the Mean Value Theorem to prove fundamental properties of derivatives. This video is specifically designed for University students (Math & Engineering) and anyone deep-diving into Real Analysis.

In this video, we cover:
The Constant Function Theorem: Proving that if f'(x)=0 for all x in an interval, then f(x) must be a constant.
The Identity Criterion: Proving that if two functions have the same derivative
(f ′(x)=g'(x)), they differ only by a constant C.
Key Concepts Explained:
Understanding the hypothesis of LMVT.
Step-by-step logical deduction for university examinations.
The link between slopes and constant values in Real Analysis.
About the Channel: Calculus Craze provides in-depth tutorials on complex mathematical concepts to help students excel in their academic journeys.
Calculus, Real Analysis, Lagrange Mean Value Theorem, LMVT Proofs, Constant Function Theorem, Derivative of a Constant, Calculus 1 for Engineers, Abdul Fatah Khalil Rajri, Calculus Craze, Mean Value Theorem Applications, University Math Tutorial, Engineering Mathematics, Mathematical Analysis, Calculus Proofs, If f'(x)=0 then f(x) is constant, f'(x)=g'(x) proof, Rolle's Theorem vs LMVT, Limits and Continuity, Derivatives, Higher Mathematics, Undergraduate Math, STEM Education, Calculus Exam Prep, Real Analysis Proofs, Mathematics for Physicists.

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