Question 2 Given the function of two variables f(x,y) = 8x2+6xy +4y2+5 a) Find the gradient vector Vf(x,y). Use Lagrange Multipliers to find the extreme value(s) of the function f subject to the constraint 3x + y +7=0. b)' c)! ] Verify that 1 23 f(x,y) = 8 3y)²+y+5 and 8 show that f has minimum and no maximum.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 2
Given the function of two
variables
f(x,y) = 8x2 +6xy +4y2 + 5
a)
Find the gradient vector Vf(x,y).
Use Lagrange Multipliers to find
the extreme value(s) of the function f
subject to the constraint 3x + y +7=0.
b)'
c)!
] Verify that
1
f(x,y) =
(8x +3y)2+
8
23
v2+5 and
8
show that f has minimum and no
maximum.
Transcribed Image Text:Question 2 Given the function of two variables f(x,y) = 8x2 +6xy +4y2 + 5 a) Find the gradient vector Vf(x,y). Use Lagrange Multipliers to find the extreme value(s) of the function f subject to the constraint 3x + y +7=0. b)' c)! ] Verify that 1 f(x,y) = (8x +3y)2+ 8 23 v2+5 and 8 show that f has minimum and no maximum.
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