Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² + xy - y² + 21y Step 1 The function z = f(x, y) describes a surface in three dimensions. Therefore, for a maximum or minimum point to exist, a horizontal plane must be tangent to the surface at that point. For a plane to be horizontal, every line on the plane will also be horizontal. Therefore, tangent lines parallel to the x- and y-axes will have zero slopes. Thus, to find any critical points, we need to determine where both zx and zy are equal to zero. Begin by finding the partial derivatives of z with respect to x and y. y-2r Fantastic job! Step 2 Zx=y-2x Zy= - 2y + 21 Step 4 Next, we find any points that satisfy both zx = 0 and 2y = 0. Setting Zx equal to zero allows us to easily express y in terms of x. -2x + y = 0 x-2y+21 Great job! y Step 3 Now, we can set zy= 0, substitute 2x for y, and solve for x. 2x 2x 2x x Impressive work! +21=0 -3.x -21 x=7✔ 7 Nicely done.

Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² + xy - y² + 21y Step 1 The function z = f(x, y) describes a surface in three dimensions. Therefore, for a maximum or minimum point to exist, a horizontal plane must be tangent to the surface at that point. For a plane to be horizontal, every line on the plane will also be horizontal. Therefore, tangent lines parallel to the x- and y-axes will have zero slopes. Thus, to find any critical points, we need to determine where both zx and zy are equal to zero. Begin by finding the partial derivatives of z with respect to x and y. y-2r Fantastic job! Step 2 Zx=y-2x Zy= - 2y + 21 Step 4 Next, we find any points that satisfy both zx = 0 and 2y = 0. Setting Zx equal to zero allows us to easily express y in terms of x. -2x + y = 0 x-2y+21 Great job! y Step 3 Now, we can set zy= 0, substitute 2x for y, and solve for x. 2x 2x 2x x Impressive work! +21=0 -3.x -21 x=7✔ 7 Nicely done.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
Question
100%

PLEASE SHOW ALL WORK! THANK YOU.

Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² + xy - y² + 21y Step 1 The function z = f(x, y) describes a surface in three dimensions. Therefore, for a maximum or minimum point to exist, a horizontal plane must be tangent to the surface at that point. For a plane to be horizontal, every line on the plane will also be horizontal. Therefore, tangent lines parallel to the x- and y-axes will have zero slopes. Thus, to find any critical points, we need to determine where both zx and zy are equal to zero. Begin by finding the partial derivatives of z with respect to x and y. y-2r Fantastic job! Zx = Zy = 2x - 2y + 21 Step 2 Next, we find any points that satisfy both zx = 0 and zy = 0. Setting zx equal to zero allows us to easily express y in terms of x. -2x + y = 0 y = 2x x-2y+21 Great job! (x, y, z) = Step 3 Now, we can set zy = 0, substitute 2x for y, and solve for x. 2x 2x X 2x Impressive work! X + 21 = 0 -3x -21 x=7 ✔ Step 4 Use the value of x to solve for y. Then use those values in the original equation to solve for z and determine the critical point. 7 Nicely done.
Transcribed Image Text:Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² + xy - y² + 21y Step 1 The function z = f(x, y) describes a surface in three dimensions. Therefore, for a maximum or minimum point to exist, a horizontal plane must be tangent to the surface at that point. For a plane to be horizontal, every line on the plane will also be horizontal. Therefore, tangent lines parallel to the x- and y-axes will have zero slopes. Thus, to find any critical points, we need to determine where both zx and zy are equal to zero. Begin by finding the partial derivatives of z with respect to x and y. y-2r Fantastic job! Zx = Zy = 2x - 2y + 21 Step 2 Next, we find any points that satisfy both zx = 0 and zy = 0. Setting zx equal to zero allows us to easily express y in terms of x. -2x + y = 0 y = 2x x-2y+21 Great job! (x, y, z) = Step 3 Now, we can set zy = 0, substitute 2x for y, and solve for x. 2x 2x X 2x Impressive work! X + 21 = 0 -3x -21 x=7 ✔ Step 4 Use the value of x to solve for y. Then use those values in the original equation to solve for z and determine the critical point. 7 Nicely done.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS