Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use the method of Lagrange multipliers to optimize $f$ as indicated, subject to the given constraint(s).Maximize $f(x, y)=x y$ such that $4 x+2 y=12$

$9 / 2$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 4

The Method of Lagrange Multipliers

Partial Derivatives

Missouri State University

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

02:14

Use the method of Lagrange…

01:28

02:38

01:49

03:30

04:26

01:18

01:44

02:49

02:20

03:10

you asked to find the extreme A. Of dysfunction here? Um X. Y. X. Times Y. Um subject to the constraint. Um This is actually going to be a maximum subject to this constraint that um Let's see here that four X plus two Y minus 12 is zero. So we construct our augmented function here. Um G sex Y plus lambert times the constraint. Um Take partial derivatives. Take partial with respect to X. We get four Y. Four land plus Y partial with respect to why we get to lambda plus X. Push their respective land and we just get see back and set those all equal to zero. And that gives us three equations for three unknowns. Um They're nice and linear so we can just you know kind of use back substitution and eliminate variables. And in the end after some algebra we get that X equals three halves, Y equals three and lambda equals minus three halves. Now if we plug this back into here we obviously get nine haves. And so that's the maximum of this function. Subject to this constraint.

View More Answers From This Book

Find Another Textbook

02:09

Using the derivative, verify that the function in the indicated exercise is …

03:05

Find an exponential function determined by the data in Table 7

01:26

Evaluate the given definite integral.$\int_{-1}^{2}\left(3 x^{2}-2 x+4\r…

03:52

Use the properties of logarithms to find the derivative. Hint: It might be e…

01:46

01:31

Solve for $x.$$$4^{x}=23$$

04:56

Determine the area of the region between the given curves.$$f(x)=|x| \te…

01:00

Are there functions that are their own inverse?

01:37

Determine the equation of the tangent line at the given $x$ -coordinate.…

01:03

If $f^{\prime}(x)=2 e^{x},$ sketch the family of solutions.