BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Think About It In Exercises 19–24, determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point (x0, y0).

f x x ( x 0 , y 0 ) = 3 , f y y ( x 0 , y 0 ) = 8 , f x y ( x 0 , y 0 ) = 2

To determine

Whether the function f(x,y) at the critical point (x0,y0) has a relative maximum, a relative minimum, a saddle point or insufficient information to determine the nature of the function.

Explanation

Given Information:

f(x,y) has a critical point (x0,y0) and the second partial derivatives are given as:

fxx(x0,y0)=3;fyy(x0,y0)=8;fxy(x0,y0)=2

For a multivariate function f(x,y) has a critical point (a,b) which is given by

fx(a,b)=dfdx|(a,b)=0fy(a,b)=dfdy|(a,b)=0

Now to determine the relative maxima or minima of the above critical point the second partial derivative test is performed.

Define,

D=fxx(a,b)fyy(a,b)[fxy(a,b)]2

1. If D>0 and fxx(a,b)>0 then (a,b) is a relative minimum at the above critical point.

2. If D<0 and fyy(a,b)<0 then (a,b) is a relative maximum at the above critical point

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.2 P-45ESect-7.2 P-46ESect-7.2 P-47ESect-7.2 P-48ESect-7.2 P-49ESect-7.2 P-50ESect-7.2 P-51ESect-7.3 P-1CPSect-7.3 P-2CPSect-7.3 P-3CPSect-7.3 P-4CPSect-7.3 P-5CPSect-7.3 P-1SWUSect-7.3 P-2SWUSect-7.3 P-3SWUSect-7.3 P-4SWUSect-7.3 P-5SWUSect-7.3 P-6SWUSect-7.3 P-7SWUSect-7.3 P-8SWUSect-7.3 P-9SWUSect-7.3 P-10SWUSect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.3 P-33ESect-7.3 P-34ESect-7.3 P-35ESect-7.3 P-36ESect-7.3 P-37ESect-7.3 P-38ESect-7.3 P-39ESect-7.3 P-40ESect-7.3 P-41ESect-7.3 P-42ESect-7.3 P-43ESect-7.3 P-44ESect-7.3 P-45ESect-7.3 P-46ESect-7.3 P-47ESect-7.3 P-48ESect-7.3 P-49ESect-7.3 P-50ESect-7.3 P-51ESect-7.3 P-53ESect-7.3 P-54ESect-7.3 P-55ESect-7.4 P-1CPSect-7.4 P-2CPSect-7.4 P-3CPSect-7.4 P-4CPSect-7.4 P-5CPSect-7.4 P-6CPSect-7.4 P-7CPSect-7.4 P-1SWUSect-7.4 P-2SWUSect-7.4 P-3SWUSect-7.4 P-4SWUSect-7.4 P-5SWUSect-7.4 P-6SWUSect-7.4 P-7SWUSect-7.4 P-8SWUSect-7.4 P-9SWUSect-7.4 P-10SWUSect-7.4 P-1ESect-7.4 P-2ESect-7.4 P-3ESect-7.4 P-4ESect-7.4 P-5ESect-7.4 P-6ESect-7.4 P-7ESect-7.4 P-8ESect-7.4 P-9ESect-7.4 P-10ESect-7.4 P-11ESect-7.4 P-12ESect-7.4 P-13ESect-7.4 P-14ESect-7.4 P-15ESect-7.4 P-16ESect-7.4 P-17ESect-7.4 P-18ESect-7.4 P-19ESect-7.4 P-20ESect-7.4 P-21ESect-7.4 P-22ESect-7.4 P-23ESect-7.4 P-24ESect-7.4 P-25ESect-7.4 P-26ESect-7.4 P-27ESect-7.4 P-28ESect-7.4 P-29ESect-7.4 P-30ESect-7.4 P-31ESect-7.4 P-32ESect-7.4 P-33ESect-7.4 P-34ESect-7.4 P-35ESect-7.4 P-36ESect-7.4 P-37ESect-7.4 P-38ESect-7.4 P-39ESect-7.4 P-40ESect-7.4 P-41ESect-7.4 P-42ESect-7.4 P-43ESect-7.4 P-44ESect-7.4 P-45ESect-7.4 P-46ESect-7.4 P-47ESect-7.4 P-48ESect-7.4 P-49ESect-7.4 P-50ESect-7.4 P-51ESect-7.4 P-52ESect-7.4 P-53ESect-7.4 P-54ESect-7.4 P-55ESect-7.4 P-56ESect-7.4 P-57ESect-7.4 P-58ESect-7.4 P-59ESect-7.4 P-60ESect-7.4 P-61ESect-7.4 P-62ESect-7.4 P-63ESect-7.4 P-64ESect-7.4 P-65ESect-7.4 P-66ESect-7.4 P-67ESect-7.4 P-68ESect-7.4 P-69ESect-7.4 P-71ESect-7.4 P-72ESect-7.4 P-73ESect-7.5 P-1CPSect-7.5 P-2CPSect-7.5 P-3CPSect-7.5 P-4CPSect-7.5 P-5CPSect-7.5 P-1SWUSect-7.5 P-2SWUSect-7.5 P-3SWUSect-7.5 P-4SWUSect-7.5 P-5SWUSect-7.5 P-6SWUSect-7.5 P-7SWUSect-7.5 P-8SWUSect-7.5 P-9SWUSect-7.5 P-10SWUSect-7.5 P-11SWUSect-7.5 P-12SWUSect-7.5 P-13SWUSect-7.5 P-14SWUSect-7.5 P-1ESect-7.5 P-2ESect-7.5 P-3ESect-7.5 P-4ESect-7.5 P-5ESect-7.5 P-6ESect-7.5 P-7ESect-7.5 P-8ESect-7.5 P-9ESect-7.5 P-10ESect-7.5 P-11ESect-7.5 P-12ESect-7.5 P-13ESect-7.5 P-14ESect-7.5 P-15ESect-7.5 P-16ESect-7.5 P-17ESect-7.5 P-18ESect-7.5 P-19ESect-7.5 P-20ESect-7.5 P-21ESect-7.5 P-22ESect-7.5 P-23ESect-7.5 P-24ESect-7.5 P-25ESect-7.5 P-26ESect-7.5 P-27ESect-7.5 P-28ESect-7.5 P-29ESect-7.5 P-30ESect-7.5 P-31ESect-7.5 P-32ESect-7.5 P-33ESect-7.5 P-34ESect-7.5 P-35ESect-7.5 P-36ESect-7.5 P-37ESect-7.5 P-38ESect-7.5 P-39ESect-7.5 P-40ESect-7.5 P-41ESect-7.5 P-42ESect-7.5 P-43ESect-7.5 P-44ESect-7.5 P-45ESect-7.5 P-46ESect-7.5 P-47ESect-7.5 P-48ESect-7.5 P-49ESect-7.5 P-50ESect-7.5 P-51ESect-7.5 P-53ESect-7.5 P-54ESect-7.5 P-55ESect-7.5 P-56ESect-7.5 P-1QYSect-7.5 P-2QYSect-7.5 P-3QYSect-7.5 P-4QYSect-7.5 P-5QYSect-7.5 P-6QYSect-7.5 P-7QYSect-7.5 P-8QYSect-7.5 P-9QYSect-7.5 P-10QYSect-7.5 P-11QYSect-7.5 P-12QYSect-7.5 P-13QYSect-7.5 P-14QYSect-7.5 P-15QYSect-7.5 P-16QYSect-7.5 P-17QYSect-7.5 P-18QYSect-7.5 P-19QYSect-7.5 P-20QYSect-7.5 P-21QYSect-7.5 P-22QYSect-7.5 P-23QYSect-7.5 P-24QYSect-7.5 P-25QYSect-7.5 P-26QYSect-7.6 P-1CPSect-7.6 P-2CPSect-7.6 P-3CPSect-7.6 P-4CPSect-7.6 P-1SWUSect-7.6 P-2SWUSect-7.6 P-3SWUSect-7.6 P-4SWUSect-7.6 P-5SWUSect-7.6 P-6SWUSect-7.6 P-7SWUSect-7.6 P-8SWUSect-7.6 P-9SWUSect-7.6 P-10SWUSect-7.6 P-1ESect-7.6 P-2ESect-7.6 P-3ESect-7.6 P-4ESect-7.6 P-5ESect-7.6 P-6ESect-7.6 P-7ESect-7.6 P-8ESect-7.6 P-9ESect-7.6 P-10ESect-7.6 P-11ESect-7.6 P-12ESect-7.6 P-13ESect-7.6 P-14ESect-7.6 P-15ESect-7.6 P-16ESect-7.6 P-17ESect-7.6 P-18ESect-7.6 P-19ESect-7.6 P-20ESect-7.6 P-21ESect-7.6 P-22ESect-7.6 P-23ESect-7.6 P-24ESect-7.6 P-25ESect-7.6 P-26ESect-7.6 P-27ESect-7.6 P-28ESect-7.6 P-29ESect-7.6 P-30ESect-7.6 P-31ESect-7.6 P-32ESect-7.6 P-33ESect-7.6 P-34ESect-7.6 P-35ESect-7.6 P-36ESect-7.6 P-37ESect-7.6 P-38ESect-7.6 P-39ESect-7.6 P-40ESect-7.6 P-41ESect-7.6 P-42ESect-7.6 P-43ESect-7.6 P-44ESect-7.6 P-45ESect-7.7 P-1CPSect-7.7 P-2CPSect-7.7 P-3CPSect-7.7 P-1SWUSect-7.7 P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 P-12ESect-7.8 P-13ESect-7.8 P-14ESect-7.8 P-15ESect-7.8 P-16ESect-7.8 P-17ESect-7.8 P-18ESect-7.8 P-19ESect-7.8 P-20ESect-7.8 P-21ESect-7.8 P-22ESect-7.8 P-23ESect-7.8 P-24ESect-7.8 P-25ESect-7.8 P-26ESect-7.8 P-27ESect-7.8 P-28ESect-7.8 P-29ESect-7.8 P-30ESect-7.8 P-31ESect-7.8 P-32ESect-7.8 P-33ESect-7.8 P-34ESect-7.8 P-35ESect-7.8 P-36ESect-7.8 P-37ESect-7.8 P-38ESect-7.8 P-39ESect-7.8 P-40ESect-7.8 P-41ESect-7.8 P-42ESect-7.8 P-43ESect-7.8 P-44ESect-7.8 P-45ESect-7.8 P-46ESect-7.8 P-47ESect-7.8 P-48ESect-7.8 P-49ESect-7.8 P-50ESect-7.8 P-51ESect-7.8 P-52ESect-7.8 P-53ESect-7.8 P-54ESect-7.8 P-55ESect-7.8 P-56ESect-7.8 P-57ESect-7.8 P-58ESect-7.8 P-59ESect-7.8 P-60ESect-7.9 P-1CPSect-7.9 P-2CPSect-7.9 P-3CPSect-7.9 P-4CPSect-7.9 P-5CPSect-7.9 P-1SWUSect-7.9 P-2SWUSect-7.9 P-3SWUSect-7.9 P-4SWUSect-7.9 P-5SWUSect-7.9 P-6SWUSect-7.9 P-7SWUSect-7.9 P-8SWUSect-7.9 P-9SWUSect-7.9 P-10SWUSect-7.9 P-1ESect-7.9 P-2ESect-7.9 P-3ESect-7.9 P-4ESect-7.9 P-5ESect-7.9 P-6ESect-7.9 P-7ESect-7.9 P-8ESect-7.9 P-9ESect-7.9 P-10ESect-7.9 P-11ESect-7.9 P-12ESect-7.9 P-13ESect-7.9 P-14ESect-7.9 P-15ESect-7.9 P-16ESect-7.9 P-17ESect-7.9 P-18ESect-7.9 P-19ESect-7.9 P-20ESect-7.9 P-21ESect-7.9 P-22ESect-7.9 P-23ESect-7.9 P-24ESect-7.9 P-25ESect-7.9 P-26ESect-7.9 P-27ESect-7.9 P-28ESect-7.9 P-29ESect-7.9 P-30ESect-7.9 P-31ESect-7.9 P-32ESect-7.9 P-33ESect-7.9 P-34ESect-7.9 P-35ESect-7.9 P-36ECh-7 P-1RECh-7 P-2RECh-7 P-3RECh-7 P-4RECh-7 P-5RECh-7 P-6RECh-7 P-7RECh-7 P-8RECh-7 P-9RECh-7 P-10RECh-7 P-11RECh-7 P-12RECh-7 P-13RECh-7 P-14RECh-7 P-15RECh-7 P-16RECh-7 P-17RECh-7 P-18RECh-7 P-19RECh-7 P-20RECh-7 P-21RECh-7 P-22RECh-7 P-23RECh-7 P-24RECh-7 P-25RECh-7 P-26RECh-7 P-27RECh-7 P-28RECh-7 P-29RECh-7 P-30RECh-7 P-31RECh-7 P-32RECh-7 P-33RECh-7 P-34RECh-7 P-35RECh-7 P-36RECh-7 P-37RECh-7 P-38RECh-7 P-39RECh-7 P-40RECh-7 P-41RECh-7 P-42RECh-7 P-43RECh-7 P-44RECh-7 P-45RECh-7 P-46RECh-7 P-47RECh-7 P-48RECh-7 P-49RECh-7 P-50RECh-7 P-51RECh-7 P-52RECh-7 P-53RECh-7 P-54RECh-7 P-55RECh-7 P-56RECh-7 P-57RECh-7 P-58RECh-7 P-59RECh-7 P-60RECh-7 P-61RECh-7 P-62RECh-7 P-63RECh-7 P-64RECh-7 P-65RECh-7 P-66RECh-7 P-67RECh-7 P-68RECh-7 P-69RECh-7 P-70RECh-7 P-71RECh-7 P-72RECh-7 P-73RECh-7 P-74RECh-7 P-75RECh-7 P-76RECh-7 P-77RECh-7 P-78RECh-7 P-79RECh-7 P-80RECh-7 P-81RECh-7 P-82RECh-7 P-83RECh-7 P-84RECh-7 P-85RECh-7 P-86RECh-7 P-87RECh-7 P-88RECh-7 P-89RECh-7 P-90RECh-7 P-91RECh-7 P-92RECh-7 P-93RECh-7 P-94RECh-7 P-95RECh-7 P-96RECh-7 P-97RECh-7 P-98RECh-7 P-99RECh-7 P-100RECh-7 P-101RECh-7 P-102RECh-7 P-103RECh-7 P-104RECh-7 P-1TYSCh-7 P-2TYSCh-7 P-3TYSCh-7 P-4TYSCh-7 P-5TYSCh-7 P-6TYSCh-7 P-7TYSCh-7 P-8TYSCh-7 P-9TYSCh-7 P-10TYSCh-7 P-11TYSCh-7 P-12TYSCh-7 P-13TYSCh-7 P-14TYSCh-7 P-15TYSCh-7 P-16TYSCh-7 P-17TYSCh-7 P-18TYSCh-7 P-19TYSCh-7 P-20TYSCh-7 P-21TYSCh-7 P-22TYS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find all possible real solutions of each equation in Exercises 3144. x3+6x2+11x+6=0

Finite Mathematics and Applied Calculus (MindTap Course List)

What is the lowest score in the following distribution?

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

Find an equation of the line that has slope 2 and passes through the midpoint of the line segment joining the p...

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

In problems 23-36, use the rules of exponents to simplify so that only positive exponents remain. 34.

Mathematical Applications for the Management, Life, and Social Sciences

sinx=ex+ex2

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