Explanation Result used: Let the partial derivatives f x x , f y y and f x y of the function z = f ( x , y ) exists in the circular region contained in the xy -plane with center ( a , b ) and f x ( a , b ) = 0 , f y ( a , b ) = 0 and the discriminant D = f x x ( a , b ) ⋅ f y y ( a , b ) − [ f x y ( a , b ) ] 2 . (a) The function has relative maximum at ( a , b ) if D > 0 and f x x ( a , b ) < 0 . (b) The function has relative minimum at ( a , b ) if D > 0 and f x x ( a , b ) > 0 . (c) If D < 0 , then f ( a , b ) is a saddle point (neither a maximum nor a minimum) (d) If D = 0 , then the test fail. Calculation: The given function is, z = 1 2 x 2 + 1 2 y 2 + 2 x y − 5 x − 7 y + 10 . Calculate the partial derivative of the above function with respect to x . z x = ∂ ∂ x ( 1 2 x 2 + 1 2 y 2 + 2 x y − 5 x − 7 y + 10 ) = ∂ ∂ x ( 1 2 x 2 ) + ∂ ∂ x ( 1 2 y 2 ) + ∂ ∂ x ( 2 x y ) − ∂ ∂ x ( 5 x ) − ∂ ∂ x ( 7 y ) + ∂ ∂ x ( 10 ) = x + 0 + 2 y − 5 − 0 + 0 = x + 2 y − 5 Again, take the partial derivative of the function z x with respect to x . z x x = ∂ ∂ x ( z x ) = ∂ ∂ x ( x + 2 y − 5 ) = ∂ ∂ x ( x ) + ∂ ∂ x ( 2 y ) − ∂ ∂ x ( 5 ) = 1 That is, z x x = 1 (1) Calculate the partial derivative of the function z with respect to y . z y = ∂ ∂ y ( 1 2 x 2 + 1 2 y 2 + 2 x y − 5 x − 7 y + 10 ) = ∂ ∂ y ( 1 2 x 2 ) + ∂ ∂ y ( 1 2 y 2 ) + ∂ ∂ y ( 2 x y ) − ∂ ∂ y ( 5 x ) − ∂ ∂ y ( 7 y ) + ∂ ∂ y ( 10 ) = y + 2 x − 0 − 7 + 0 = y + 2 x − 7 Again, take the partial derivative of the function z y with respect to y

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 17, Problem 49RE

To determine

To find: The points such that the function z=12x2+12y2+2xy−5x−7y+10 attains relative extrema and identify any saddle points.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17, Problem 48RE

Chapter 17, Problem 50RE

Students have asked these similar questions

1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b) the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the 8-second period. t 0 2 4 6 8 V 10 15 12 10 16 2. Find the midpoint rule approximation for (a) n = 4 +5 x²dx using n subintervals. 1° 2 (b) n = 8 36 32 28 36 32 28 24 24 20 20 16 16 12 8- 4 1 2 3 4 5 6 12 8 4 1 2 3 4 5 6

= 5 37 A 4 8 0.5 06 9

Consider the following system of equations, Ax=b : x+2y+3z - w = 2 2x4z2w = 3 -x+6y+17z7w = 0 -9x-2y+13z7w = -14 a. Find the solution to the system. Write it as a parametric equation. You can use a computer to do the row reduction. b. What is a geometric description of the solution? Explain how you know. c. Write the solution in vector form? d. What is the solution to the homogeneous system, Ax=0?

Chapter 17 Solutions

Finite Mathematics and Calculus with Applications

Ch. 17.1 - For the function in Example 1, find f(2, 3)....Ch. 17.1 - Prob. 2YT Ch. 17.1 - Prob. 3YT Ch. 17.1 - Prob. 4YT Ch. 17.1 - Prob. 1WE Ch. 17.1 - Prob. 2WE Ch. 17.1 - Prob. 3WE Ch. 17.1 - Prob. 4WE Ch. 17.1 - Prob. 5WE Ch. 17.1 - Prob. 6WE

Ch. 17.1 - Let f(x, y) = 2x 3y + 5. Find the following....Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Graph the first-octant portion of each plane. 9.2x...Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Match each equation in Exercises 2328 with its...Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Match each equation in Exercises 2328 with its...Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Production Find the level curve at a production of...Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Individual Retirement Accounts The multiplier...Ch. 17.1 - Individual Retirement Accounts The multiplier...Ch. 17.1 - Heat Loss The rate of heal loss (in watts) in...Ch. 17.1 - Prob. 41E Ch. 17.1 - Prob. 42E Ch. 17.1 - Pollution Intolerance According to research at the...Ch. 17.1 - Dengue Fever In tropical regions, dengue fever is...Ch. 17.1 - Prob. 45E Ch. 17.1 - Prob. 46E Ch. 17.1 - Prob. 47E Ch. 17.1 - Prob. 48E Ch. 17.1 - Prob. 49E Ch. 17.1 - Prob. 50E Ch. 17.1 - Prob. 51E Ch. 17.2 - Prob. 1YT Ch. 17.2 - Prob. 2YT Ch. 17.2 - Prob. 3YT Ch. 17.2 - Prob. 4YT Ch. 17.2 - Prob. 1WE Ch. 17.2 - Prob. 2WE Ch. 17.2 - Prob. 3WE Ch. 17.2 - Prob. 4WE Ch. 17.2 - Prob. 5WE Ch. 17.2 - Prob. 6WE Ch. 17.2 - Prob. 7WE Ch. 17.2 - Prob. 8WE Ch. 17.2 - Prob. 1E Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.2 - Prob. 4E Ch. 17.2 - Prob. 5E Ch. 17.2 - Prob. 6E Ch. 17.2 - Prob. 7E Ch. 17.2 - Prob. 8E Ch. 17.2 - Prob. 9E Ch. 17.2 - Prob. 10E Ch. 17.2 - Prob. 11E Ch. 17.2 - Prob. 12E Ch. 17.2 - Prob. 13E Ch. 17.2 - Prob. 14E Ch. 17.2 - Prob. 15E Ch. 17.2 - Prob. 16E Ch. 17.2 - Prob. 17E Ch. 17.2 - Prob. 18E Ch. 17.2 - Prob. 19E Ch. 17.2 - Prob. 20E Ch. 17.2 - Prob. 21E Ch. 17.2 - Prob. 22E Ch. 17.2 - Prob. 23E Ch. 17.2 - Prob. 24E Ch. 17.2 - Prob. 25E Ch. 17.2 - Prob. 26E Ch. 17.2 - Prob. 27E Ch. 17.2 - Prob. 28E Ch. 17.2 - Prob. 29E Ch. 17.2 - Prob. 30E Ch. 17.2 - Prob. 31E Ch. 17.2 - Prob. 32E Ch. 17.2 - Prob. 33E Ch. 17.2 - Prob. 34E Ch. 17.2 - Prob. 35E Ch. 17.2 - Prob. 36E Ch. 17.2 - Prob. 37E Ch. 17.2 - Prob. 38E Ch. 17.2 - Prob. 39E Ch. 17.2 - Prob. 40E Ch. 17.2 - Find fx(x,y,z),fy(x,y,z),fz(x,y,z), and fyz(x,y,z)...Ch. 17.2 - Prob. 42E Ch. 17.2 - Prob. 43E Ch. 17.2 - Prob. 44E Ch. 17.2 - Business and Economics 45.Manufacturing Cost...Ch. 17.2 - Prob. 46E Ch. 17.2 - Prob. 47E Ch. 17.2 - Prob. 48E Ch. 17.2 - Prob. 49E Ch. 17.2 - Prob. 50E Ch. 17.2 - Prob. 51E Ch. 17.2 - Prob. 52E Ch. 17.2 - Prob. 53E Ch. 17.2 - Prob. 54E Ch. 17.2 - Prob. 55E Ch. 17.2 - Prob. 56E Ch. 17.2 - Prob. 57E Ch. 17.2 - Prob. 58E Ch. 17.2 - Prob. 59E Ch. 17.2 - Prob. 60E Ch. 17.2 - Prob. 61E Ch. 17.2 - Prob. 62E Ch. 17.2 - Drug Reaction The reaction to x units of a drug t...Ch. 17.2 - Prob. 64E Ch. 17.2 - Prob. 66E Ch. 17.2 - Prob. 67E Ch. 17.2 - Prob. 68E Ch. 17.2 - Gravitational Attraction The gravitational...Ch. 17.2 - Velocity In 1931, Albert Einstein developed the...Ch. 17.2 - Prob. 71E Ch. 17.3 - Prob. 1YT Ch. 17.3 - Prob. 2YT Ch. 17.3 - Prob. 1WE Ch. 17.3 - Prob. 2WE Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - Prob. 6E Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - Prob. 13E Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - Prob. 18E Ch. 17.3 - Prob. 19E Ch. 17.3 - Prob. 20E Ch. 17.3 - Prob. 21E Ch. 17.3 - Prob. 22E Ch. 17.3 - Prob. 23E Ch. 17.3 - Figures (a)(f) show the graphs of the functions...Ch. 17.3 - Prob. 25E Ch. 17.3 - Prob. 26E Ch. 17.3 - Prob. 27E Ch. 17.3 - Prob. 28E Ch. 17.3 - Prob. 29E Ch. 17.3 - Prob. 30E Ch. 17.3 - Prob. 31E Ch. 17.3 - Prob. 32E Ch. 17.3 - Prob. 33E Ch. 17.3 - Prob. 34E Ch. 17.3 - Prob. 35E Ch. 17.3 - Prob. 36E Ch. 17.3 - Prob. 37E Ch. 17.3 - Prob. 38E Ch. 17.3 - Prob. 39E Ch. 17.3 - Prob. 40E Ch. 17.3 - Prob. 42E Ch. 17.4 - Prob. 1YT Ch. 17.4 - Prob. 1WE Ch. 17.4 - Prob. 2WE Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Find the relative maxima or minima in Exercises...Ch. 17.4 - Prob. 11E Ch. 17.4 - Find positive numbers x and y such that x + y = 48...Ch. 17.4 - Prob. 13E Ch. 17.4 - Prob. 14E Ch. 17.4 - Find the maximum and minimum values of f(x, y) =x3...Ch. 17.4 - Prob. 16E Ch. 17.4 - Prob. 17E Ch. 17.4 - Prob. 18E Ch. 17.4 - Prob. 19E Ch. 17.4 - Prob. 20E Ch. 17.4 - Prob. 21E Ch. 17.4 - Discuss the advantages and disadvantages of the...Ch. 17.4 - Prob. 23E Ch. 17.4 - Prob. 24E Ch. 17.4 - Prob. 25E Ch. 17.4 - Prob. 26E Ch. 17.4 - Prob. 27E Ch. 17.4 - Prob. 28E Ch. 17.4 - Prob. 29E Ch. 17.4 - Prob. 30E Ch. 17.4 - Prob. 31E Ch. 17.4 - Prob. 32E Ch. 17.4 - Prob. 33E Ch. 17.4 - Prob. 34E Ch. 17.4 - Prob. 35E Ch. 17.4 - Prob. 36E Ch. 17.4 - Prob. 37E Ch. 17.4 - Prob. 38E Ch. 17.4 - Prob. 39E Ch. 17.4 - Prob. 40E Ch. 17.4 - Prob. 41E Ch. 17.4 - Prob. 42E Ch. 17.5 - Prob. 1YT Ch. 17.5 - Prob. 2YT Ch. 17.5 - Prob. 3YT Ch. 17.5 - Prob. 1WE Ch. 17.5 - Prob. 2WE Ch. 17.5 - Prob. 3WE Ch. 17.5 - Prob. 4WE Ch. 17.5 - Prob. 1E Ch. 17.5 - Prob. 2E Ch. 17.5 - Prob. 3E Ch. 17.5 - Prob. 4E Ch. 17.5 - Prob. 5E Ch. 17.5 - Prob. 6E Ch. 17.5 - Prob. 7E Ch. 17.5 - Prob. 8E Ch. 17.5 - Prob. 9E Ch. 17.5 - Prob. 10E Ch. 17.5 - Prob. 11E Ch. 17.5 - Prob. 12E Ch. 17.5 - Prob. 13E Ch. 17.5 - Prob. 14E Ch. 17.5 - Prob. 15E Ch. 17.5 - Prob. 16E Ch. 17.5 - Volume of a Coating An industrial coaling 0.1 in....Ch. 17.5 - Prob. 18E Ch. 17.5 - Prob. 19E Ch. 17.5 - Prob. 20E Ch. 17.5 - Prob. 21E Ch. 17.5 - Prob. 22E Ch. 17.5 - Prob. 23E Ch. 17.5 - Prob. 24E Ch. 17.5 - Life Span As we saw in Exercise 62 of Section...Ch. 17.5 - Prob. 26E Ch. 17.5 - Prob. 27E Ch. 17.5 - Prob. 28E Ch. 17.5 - Prob. 29E Ch. 17.5 - Prob. 30E Ch. 17.5 - Prob. 31E Ch. 17.5 - Prob. 32E Ch. 17.5 - Prob. 33E Ch. 17.5 - Prob. 34E Ch. 17.5 - Prob. 35E Ch. 17.6 - Prob. 1YT Ch. 17.6 - Evaluate 02[13(6x2y2+4xy+8x3+10y4+3)dy]dx and then...Ch. 17.6 - Prob. 3YT Ch. 17.6 - Prob. 4YT Ch. 17.6 - Prob. 5YT Ch. 17.6 - Prob. 1WE Ch. 17.6 - Evaluate each definite integral. W2.23x+6dx Ch. 17.6 - Prob. 3WE Ch. 17.6 - Prob. 4WE Ch. 17.6 - Prob. 5WE Ch. 17.6 - Prob. 6WE Ch. 17.6 - Prob. 1E Ch. 17.6 - Prob. 2E Ch. 17.6 - Prob. 3E Ch. 17.6 - Prob. 4E Ch. 17.6 - Prob. 5E Ch. 17.6 - Prob. 6E Ch. 17.6 - Prob. 7E Ch. 17.6 - Prob. 8E Ch. 17.6 - Prob. 9E Ch. 17.6 - Prob. 10E Ch. 17.6 - Prob. 11E Ch. 17.6 - Prob. 12E Ch. 17.6 - Prob. 13E Ch. 17.6 - Prob. 14E Ch. 17.6 - Prob. 15E Ch. 17.6 - Prob. 16E Ch. 17.6 - Prob. 17E Ch. 17.6 - Prob. 18E Ch. 17.6 - Prob. 19E Ch. 17.6 - Prob. 20E Ch. 17.6 - Prob. 21E Ch. 17.6 - Prob. 22E Ch. 17.6 - Prob. 23E Ch. 17.6 - Prob. 24E Ch. 17.6 - Prob. 25E Ch. 17.6 - Prob. 26E Ch. 17.6 - Prob. 27E Ch. 17.6 - Prob. 28E Ch. 17.6 - Prob. 29E Ch. 17.6 - Prob. 30E Ch. 17.6 - Prob. 31E Ch. 17.6 - Prob. 32E Ch. 17.6 - Prob. 33E Ch. 17.6 - Prob. 34E Ch. 17.6 - Prob. 35E Ch. 17.6 - Prob. 36E Ch. 17.6 - Prob. 37E Ch. 17.6 - Prob. 38E Ch. 17.6 - Prob. 39E Ch. 17.6 - Prob. 40E Ch. 17.6 - Prob. 41E Ch. 17.6 - Prob. 42E Ch. 17.6 - Prob. 43E Ch. 17.6 - Use the region R with the indicated boundaries to...Ch. 17.6 - Prob. 45E Ch. 17.6 - Prob. 46E Ch. 17.6 - Prob. 47E Ch. 17.6 - Prob. 48E Ch. 17.6 - Prob. 49E Ch. 17.6 - Prob. 50E Ch. 17.6 - Prob. 51E Ch. 17.6 - Prob. 52E Ch. 17.6 - Prob. 53E Ch. 17.6 - Prob. 54E Ch. 17.6 - Prob. 55E Ch. 17.6 - Prob. 56E Ch. 17.6 - Prob. 57E Ch. 17.6 - Prob. 58E Ch. 17.6 - Prob. 59E Ch. 17.6 - Prob. 60E Ch. 17.6 - Prob. 61E Ch. 17.6 - Prob. 62E Ch. 17.6 - Prob. 63E Ch. 17.6 - Prob. 64E Ch. 17.6 - Prob. 65E Ch. 17.6 - Prob. 66E Ch. 17.6 - Prob. 67E Ch. 17.6 - Prob. 68E Ch. 17.6 - Prob. 69E Ch. 17.6 - Time In Exercise 39 of Section 17.3, we saw that...Ch. 17.6 - Profit In Exercise 38 of Section 17.3, we saw that...Ch. 17 - Determine whether each of the following statements...Ch. 17 - Prob. 2RE Ch. 17 - Prob. 3RE Ch. 17 - Prob. 4RE Ch. 17 - Prob. 5RE Ch. 17 - Prob. 6RE Ch. 17 - Prob. 7RE Ch. 17 - Prob. 8RE Ch. 17 - Prob. 9RE Ch. 17 - Prob. 10RE Ch. 17 - Prob. 11RE Ch. 17 - Prob. 12RE Ch. 17 - Prob. 13RE Ch. 17 - Prob. 14RE Ch. 17 - Prob. 15RE Ch. 17 - Prob. 16RE Ch. 17 - Prob. 17RE Ch. 17 - Prob. 18RE Ch. 17 - Prob. 19RE Ch. 17 - Prob. 20RE Ch. 17 - Prob. 21RE Ch. 17 - Prob. 22RE Ch. 17 - Prob. 23RE Ch. 17 - Prob. 24RE Ch. 17 - Prob. 25RE Ch. 17 - Prob. 26RE Ch. 17 - Prob. 27RE Ch. 17 - Prob. 28RE Ch. 17 - Prob. 29RE Ch. 17 - Prob. 30RE Ch. 17 - Prob. 31RE Ch. 17 - Prob. 32RE Ch. 17 - Prob. 33RE Ch. 17 - Prob. 34RE Ch. 17 - Prob. 35RE Ch. 17 - Prob. 36RE Ch. 17 - Prob. 37RE Ch. 17 - Prob. 38RE Ch. 17 - Prob. 39RE Ch. 17 - Prob. 40RE Ch. 17 - Prob. 41RE Ch. 17 - Prob. 42RE Ch. 17 - Prob. 43RE Ch. 17 - Prob. 44RE Ch. 17 - Prob. 45RE Ch. 17 - Prob. 46RE Ch. 17 - Prob. 47RE Ch. 17 - Prob. 48RE Ch. 17 - Prob. 49RE Ch. 17 - Prob. 50RE Ch. 17 - Prob. 51RE Ch. 17 - Prob. 52RE Ch. 17 - Prob. 53RE Ch. 17 - Prob. 54RE Ch. 17 - Prob. 55RE Ch. 17 - Prob. 56RE Ch. 17 - Prob. 57RE Ch. 17 - Prob. 58RE Ch. 17 - Evaluate dz using the given information. 59.z =...Ch. 17 - Prob. 60RE Ch. 17 - Prob. 61RE Ch. 17 - Prob. 62RE Ch. 17 - Prob. 63RE Ch. 17 - Prob. 64RE Ch. 17 - Prob. 65RE Ch. 17 - Prob. 66RE Ch. 17 - Prob. 67RE Ch. 17 - Prob. 68RE Ch. 17 - Prob. 69RE Ch. 17 - Prob. 70RE Ch. 17 - Prob. 71RE Ch. 17 - Prob. 72RE Ch. 17 - Prob. 73RE Ch. 17 - Prob. 74RE Ch. 17 - Prob. 75RE Ch. 17 - Prob. 76RE Ch. 17 - Prob. 77RE Ch. 17 - Prob. 78RE Ch. 17 - Prob. 79RE Ch. 17 - Prob. 80RE Ch. 17 - Prob. 81RE Ch. 17 - Prob. 82RE Ch. 17 - Prob. 83RE Ch. 17 - Evaluate each double integral. If the function...Ch. 17 - Prob. 85RE Ch. 17 - Prob. 86RE Ch. 17 - Prob. 87RE Ch. 17 - Prob. 88RE Ch. 17 - Prob. 89RE Ch. 17 - Prob. 90RE Ch. 17 - Prob. 91RE Ch. 17 - Prob. 92RE Ch. 17 - Prob. 93RE Ch. 17 - Prob. 94RE Ch. 17 - Prob. 95RE Ch. 17 - Prob. 96RE Ch. 17 - Profit The total profit from 1 acre of a certain...Ch. 17 - Prob. 98RE Ch. 17 - Prob. 99RE Ch. 17 - Prob. 100RE Ch. 17 - Prob. 101RE Ch. 17 - Prob. 102RE Ch. 17 - Prob. 103RE Ch. 17 - Prob. 104RE Ch. 17 - Prob. 105RE Ch. 17 - Prob. 106RE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The points such that the function z = 1 2 x 2 + 1 2 y 2 + 2 x y − 5 x − 7 y + 10 attains relative extrema and identify any saddle points.

Solution Summary: The author explains that the function has a saddle point at (3,1).

Concept explainers

Videos

To find: The points such that the function z=12x2+12y2+2xy−5x−7y+10 attains relative extrema and identify any saddle points.

Want to see the full answer?

Chapter 17 Solutions