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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7, Problem 76RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Using Lagrange Multipliers In Exercises 73-78, use Lagrange multipliers to find the indicated extremum. Assume that the variables are positive.

Minimize f ( x , y )   = 3 x 2 −   y 2

Constraint: 2 x   −   4 y   =   − 11

To determine

To calculate: The minimum value of the function f(x,y)=3x2−y2 subject to constraint

2x−4y=−11 by the application of Lagrange multipliers.

Explanation

Given Information:

The provided function is f(x,y)=3x2−y2 and the subject to constraints are 2x−4y=−11.

Formula used:

To find the maximum or minimum values of function f follow the steps as;

Step 1: Solve the provided system of equations as,

Fx(x,y,λ)=0Fy(x,y,λ)=0Fλ(x,y,λ)=0

Step 2: Next calculate the function f at each of the solution point obtained from first step where the greatest value obtained gives the maximum of function f subject to constraint g(x,y)=0 and the least value gives the minimum of function f subject to constraint g(x,y)=0.

Calculation:

First let f(x,y,z)=3x2−y2 and g(x,y,z)=2x−4y+11.

Then define a new function F as;

F(x,y,z,λ)=f(x,y,z)−λg(x,y,z)=3x2−y2−λ(2x−4y+11)

Now solve the equation by finding the partial derivatives of F with respect to x, y, z and λ as;

Fx(x,y,λ)=6x−λFy(x,y,λ)=−2y+4λFλ(x

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SOC In problem 3.6, you computed mean and median income for the 13 Canadian provinces and territories and for 1...

Essentials Of Statistics

There is some evidence that people with a visible tattoo are considered to be less attractive than are people w...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find an expression for a cubic function f if f(1) = 6 and f(l) + f(0) = f(2) = 0.

Single Variable Calculus

Health Club Membership The membership of the newly opened Venus Health Club is approximated by the function N(x...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve the differential equation using a undetermined coefficients and b variation of parameters. 4y+y=cosx

Calculus (MindTap Course List)

A random sample of n=12 individuals is selected from a population with =70 , and a treatment is administered to...

Statistics for The Behavioral Sciences (MindTap Course List)

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. xy1x1

Finite Mathematics

Critical Thinking Suppose you took random samples from three distinct age groups. Through a survey, you determi...

Understanding Basic Statistics

Consider four independent events A1, A2, A3, and A4, and let pi 5 P(Ai) for i 5 1,2,3,4. Express the probabilit...

Probability and Statistics for Engineering and the Sciences

In Exercises 47 to 54, find the number of subsets of the given set. {x | x is an odd integer between –4 and 8...

Mathematical Excursions (MindTap Course List)

For Problems 56-64, use your calculator to evaluate each numerical expression. Objective 3 (3.14)3

Intermediate Algebra

In Problems, indicate whether the given expression is one or more of the following types of numbers: rational, ...

Mathematical Applications for the Management, Life, and Social Sciences

Sketch the region and find its area (if the area is finite). 43. S={(x,y)|x1,0y1/(x3+x)}

Single Variable Calculus: Early Transcendentals

12. (See Example 4.) Prove the right distributive law in: . Example 4 For, let denote the congruence class...

Elements Of Modern Algebra

Exercises 3840 In the box shown for Exercise 38, use intuition to answer each question. a Are AB and DC paralle...

Elementary Geometry For College Students, 7e

During a line voltage surge, the normal ac voltage in- creased from 115 V to 128 V. Find the percent increase.

Elementary Technical Mathematics

In September, Tire Depot in Chicago purchased snow tires from a distributor for $48.50 each. The original marku...

Contemporary Mathematics for Business & Consumers

Graph y=x+2.

Trigonometry (MindTap Course List)

Simplifying an Expression In Exercises 127-132, write the expression in algebraic form. [Hint: Sketch a right t...

Calculus: Early Transcendental Functions (MindTap Course List)

Failure of Newton's Method In Exercises 23 and 24, apply Newtons Method using the given initial guess, and expl...

Calculus of a Single Variable

In Exercises 55 and 56, refer to the following Venn diagram, where U is the set of all tourists surveyed over a...

Finite Mathematics for the Managerial, Life, and Social Sciences

The four owners of a shop realize a loss of 240 in February. If the loss is shared equally, what number represe...

Elementary Geometry for College Students

Finding a Particular Solution: Boundary ConditionsIn Exercises 45-50, find the particular solution of the linea...

Multivariable Calculus

Orientation Describe the orientation of the parametric equations x=t2 and y=t4 for 1t1.

Calculus (MindTap Course List)

By determining the limit of Riemann sums, the exact value of dx is a) 7 b) 9 c) d) 18

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

EXPLORING CONCEPTS Transformations of Functions In Exercises 63-66, assume that f is differentiable for all x. ...

Calculus

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Study Guide for Stewart's Multivariable Calculus, 8th

During the period of time that a local university takes phone-in registrations, calls come inat the rate of one...

Statistics for Business & Economics, Revised (MindTap Course List)

If steel weighs 0.264 1b/cubic inch, what is the weight of this steel shaft? Round the answer to the nearest te...

Mathematics For Machine Technology

A sample of automobiles traversing a certain stretch of highway is selected. Each one travels at roughly a cons...

Introduction To Statistics And Data Analysis

Exercise 5-12 deal with data from the U.S. Bureau of the Census on populations of major cities. These data allo...

Mathematics: A Practical Odyssey

Explain how the existence of an interaction can influence the interpretation of main effects.

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither. 3x+6y=1,y=12x

College Algebra (MindTap Course List)

A social science researcher would like to determine the characteristics of people who live and work in small to...

Research Methods for the Behavioral Sciences (MindTap Course List)

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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