IGNOU MTE 1 2026 - Verify Lagrange's mean value theorem for the funct

Question

Verify Lagrange's mean value theorem for the function f defined by $f(x) = 2x^2 - 7x - 10$ over

09 Jan 2026

Answer :

Word Count : 285

We are asked to verify Lagrange's Mean Value Theorem (LMVT) for the function ( f(x) = 2x^2 - 7x - 10 ) over an interval. Since the interval is not explicitly given in your message, I will assume a general interval ([a, b]) for verification, and we can plug numbers once clarified. For demonstration, let's take the standard interval ([0, 3]). Lagrange's Mean Value Theorem states

_____ ______ ____ _______ _________ _______ ___.
_________ ______ __________ ____ ______ ______ ________ _____ _________ ____ __________.
_________ _________ _______ _________ ________ ______ ____ _____ ___ ____ __________.
_______ __________ ___ ________ ______ ________ ______.
_____ ____ __________ ______ ______.
__________ ___ ___ __________ ________ _________ __________ ______ ______ ____ __________ _______.
______ ____ _______ ____ ___ ____ ____.
___ _________ _________ ___ _________.
__________ ____ _________ ______ ____ _______ _______ ______ __________ _________.
_________ ________ ___ _______ ______ __________ _________ _______ ___.
_____ _________ ______ __________ __________ ________ ____ __________ __________ _________ ___ ___.
________ ___ _____ ____ _____ ________ ____.
______ _________ ___ ______ ______ _________ _____ _______ ___.
__________ ______ _____ __________ _________ ______.
________ ________ __________ _______ _____ _____ _________ ______ _________ __________ ____ _________.
_____ ________ _______ __________ ___ ___.
_______ ______ _________ _____ ______.
__________ _____ ________ _________ _________.
________ _____ __________ _______ _________ ________ _____ ___ _________ _______.
___ _____ _______ ____ ______ ________.
__________ __________ __________ ______ ______ ________ ___ ____ __________ ___ ________.
_______ ___ ____ ____ ____ _______.
_________ _____ _____ ____ ________ ________ __________.
___ _________ ________ _____ ___ _____ _________ _________ _____ _______ ________ __________.
__________ _______ _____ _______ _______ _____ _____ ___ ______ __________ ____ _______.
______ ____ ________ ____ ______ ______ _____ ______ _____.

IGNOU ACADEMY

Your IGNOU journey, made easier.