IGNOU BMTC 102 2026 - Find the extreme values of the function on the surface&nbsp

Question

Find the extreme values of the function

$f(x, y) = x^2 + y$ on the surface $x^2 + 2y^2 = 1$ .

09 Jan 2026

Answer :

Word Count : 349

We are asked to find the extreme values of (f(x, y) = x^2 + y) subject to the constraint (x^2 + 2y^2 = 1). Use the method of Lagrange multipliers. Let (\lambda) be the multiplier. Then we solve: [ \nabla f = \lambda \nabla g, \quad g(x, y) = x^2 + 2y^2 - 1 = 0 ] 1. Compute gradients: [ \nabla f = (2x, 1), \quad \nabla g = (2x, 4y) ] So the Lagrange equations are: [ 2x

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

IGNOU ACADEMY

Your IGNOU journey, made easier.