Explanation Given: The equation is F ( x , y ) = x 2 − y 2 − 16 x − 16 y . Formula used: The second partial test is: d = F x x ( x , y ) ⋅ F y y ( x , y ) − [ F x y ( x , y ) ] 2 Where, ( a ) if d > 0 , F x x ( x , y ) > 0 then F has a relative minima ( x , y ) ( b ) if d > 0 , F x x ( x , y ) < 0 then F has a realtive maxima ( x , y ) ( c ) if d < 0 , then ( x , y , f ( x , y ) ) is a saddle point Calculation: The equation of function is F ( x , y ) = x 2 − y 2 − 16 x − 16 y Therefore, F x ( x , y ) = 2 x − 16 F y ( x , y ) = − 2 x − 16 Now, critical point is the solution of equation, then F x ( x , y ) and F y ( x , y ) both equal to zero So, 2 x − 16 =

10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

See similar textbooks

Question

Chapter 13, Problem 62RE

To determine

To calculate: The all relative extrema and saddle points of the function

F(x,y)=x2−y2−16x−16y by using second partial test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 61RE

Chapter 13, Problem 63RE

Students have asked these similar questions

In Exercises 61–64, find an equation for the level surface of the function through the given point.

In Exercises 65–68, find and sketch the domain of ƒ. Then find an equation for the level curve or surface of the function passing through the given point.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. Use the information in the figure to solve Exercises 67–72. 35,000 30,000 C(x) = 10,000 + 30x 25,000 20,000 15,000 R(x) = 50x 10,000 5000 100 200 300 400 500 600 700 Radios Produced and Sold 67. How many radios must be produced and sold for the company to break even? 68. More than how many radios must be produced and sold for the company to have a profit? 69. Use the formulas shown in the voice balloons to find R(200) – C(200). Describe what this means for the company. 70. Use the formulas shown in the voice balloons to find R(300) – C(300). Describe what this means for the company. 71. a. Use the formulas shown in the voice balloons to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 10,000 radios are produced and sold. 72. a. Use the formulas shown in the voice balloons to write the company's profit function,…

Chapter 13 Solutions

Calculus

Ch. 13.1 - Determining Whether a Graph Is a Function In...Ch. 13.1 - Determine whether graph is a function. Use the...Ch. 13.1 - Prob. 3E Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - 57095-13.1-9E-Question-Digital.docx Evaluating a...Ch. 13.1 - Prob. 10E

Knowledge Booster

The all relative extrema and saddle points of the function F ( x , y ) = x 2 − y 2 − 16 x − 16 y by using second partial test.

Solution Summary: The author calculates the relative extrema and saddle points of the function F(x,y) by using second partial test.

To calculate: The all relative extrema and saddle points of the function

F(x,y)=x2−y2−16x−16y by using second partial test.

Want to see the full answer?

Chapter 13 Solutions

The all relative extrema and saddle points of the function F ( x , y ) = x 2 − y 2 − 16 x − 16 y by using second partial test.

Solution Summary: The author calculates the relative extrema and saddle points of the function F(x,y) by using second partial test.

To calculate: The all relative extrema and saddle points of the function F(x,y)=x2−y2−16x−16y by using second partial test.

Want to see the full answer?

Chapter 13 Solutions

To calculate: The all relative extrema and saddle points of the function

F(x,y)=x2−y2−16x−16y by using second partial test.