Given the function of two variables ƒ(x, y) = 4x³ − 60x² + 12xy² − 24y² +3. - - Find and classify all critical points of the function f(x, y). Question ! a) b) [1 *] Find a vector u such that the directional derivative of the function f(x, y) at th point (-1,4) in the direction of u is equal to 36√/145.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Question !
Given the function of two variables
f(x, y) = 4x³ - 60x² + 12xy² - 24y² +3.
Find and classify all critical points of the function f(x, y).
a) {
b) [I
*] Find a vector u such that the directional derivative of the function f(x, y) at the
point (-1,4) in the direction of u is equal to 36√//145.
Transcribed Image Text:Question ! Given the function of two variables f(x, y) = 4x³ - 60x² + 12xy² - 24y² +3. Find and classify all critical points of the function f(x, y). a) { b) [I *] Find a vector u such that the directional derivative of the function f(x, y) at the point (-1,4) in the direction of u is equal to 36√//145.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning