Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find all the relative extrema (local extrema) and the saddle points of the function f(x, y) = x²y — 7x² - 4xy + 28x - y² 13 + 4 Solution Step 1. Find all the critical points of the function f(x, y). We have fr = fy fz = 0 Solve fy = 0 critical points in the order that x is from smaller to larger). Hàm f(x,y) không có điểm tới hạn mà tại đó đạo hàm riêng không tồn tại. At M, D= Step 2. Apply the second partial derivatives test to verify if the function f has a relative extremum at each critical point or not. We have A = fzz D = faz fyy - fay= At N, D= we obtain 3 critical points M At P, D= .A A that implies f(x,y) , that implies f(x,y) that implies f(x,y) ◆ → + at the point M. at the point N. 29 +1. at the point P of f(x,y). (Please sort the

Find all the relative extrema (local extrema) and the saddle points of the function f(x, y) = x²y — 7x² - 4xy + 28x - y² 13 + 4 Solution Step 1. Find all the critical points of the function f(x, y). We have fr = fy fz = 0 Solve fy = 0 critical points in the order that x is from smaller to larger). Hàm f(x,y) không có điểm tới hạn mà tại đó đạo hàm riêng không tồn tại. At M, D= Step 2. Apply the second partial derivatives test to verify if the function f has a relative extremum at each critical point or not. We have A = fzz D = faz fyy - fay= At N, D= we obtain 3 critical points M At P, D= .A A that implies f(x,y) , that implies f(x,y) that implies f(x,y) ◆ → + at the point M. at the point N. 29 +1. at the point P of f(x,y). (Please sort the

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 93E
See similar textbooks
icon
Related questions
Question

Chapter 11. Partial derivatives

Q2

Find all the relative extrema (local extrema) and the saddle points of the function f(x, y) = x²y — 7x² − 4xy + 28x + 4 Solution Step 1. Find all the critical points of the function f(x, y). We have fx fy S fx = 0 | fy = 0 critical points in the order that x is from smaller to larger). Hàm f(x,y) không có điểm tới hạn mà tại đó đạo hàm riêng không tồn tại. Solve At M, D= At N, D= we obtain 3 critical points M At P, D= Step 2. Apply the second partial derivatives test to verify if the function f has a relative extremum at each critical point or not. We have A = fxx D = fxx fyy - fay A A = A = that implies f(x,y) that implies f(x,y) NO that implies f(x,y) → D, P( at the point M. at the point N. .2 13 at the point P. 2y + 1. of f(x,y). (Please sort the
Transcribed Image Text:Find all the relative extrema (local extrema) and the saddle points of the function f(x, y) = x²y — 7x² − 4xy + 28x + 4 Solution Step 1. Find all the critical points of the function f(x, y). We have fx fy S fx = 0 | fy = 0 critical points in the order that x is from smaller to larger). Hàm f(x,y) không có điểm tới hạn mà tại đó đạo hàm riêng không tồn tại. Solve At M, D= At N, D= we obtain 3 critical points M At P, D= Step 2. Apply the second partial derivatives test to verify if the function f has a relative extremum at each critical point or not. We have A = fxx D = fxx fyy - fay A A = A = that implies f(x,y) that implies f(x,y) NO that implies f(x,y) → D, P( at the point M. at the point N. .2 13 at the point P. 2y + 1. of f(x,y). (Please sort the
Expert Solution
steps

Step by step

Solved in 5 steps with 4 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
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS