Let a be a constant and f(x, y) = x³ – 3axy + y³. Determine that the following statements are "True" or "False". Türkçe: (f(x, y) = x³ – 3axy + y³ ve a bir sabit olmak üzere aşağıdaki ifadelerin "Doğru" veya "Yanlış" olduğunu belirleyiniz. ) 1. f(x, y) has a local minimum value at (a, a) for a > 0. (Türkçe: f(x,y) fonksiyonu a > 0 için (a, a)'da yerel minimuma sahiptir.) 2. f(x, y) has a local minimum value at (a, a) for a < 0. (Türkçe: ƒ(x, y) fonksiyonu a < 0 için (a, a)'da yerel minimuma sahiptir.) 3. f(x, y) has a local maximum value at (a, a) for a < 0. (Türkçe: ƒ(x, y) fonksiyonu a < 0 için (a, a)'da yerel maksimum sahiptir.) 4. f(x, y) has a local maximum value at (a, a) for a > 0. (Türkçe: f(x,y) fonksiyonu a > 0 için (a, a)'da yerel maksimum sahiptir.) 5. f(x, y) has a saddle point at (0, 0) when a = 0. (Türkçe: a = 0 iken f(x, y), (0,0)'da eyer noktasına sahiptir.) 6. f(x, y) has a saddle point at (0, 0) for a > 0. (Türkçe: a > 0 için f(x, y), (0, 0)'da eyer noktasına sahiptir.) 7. f(x, y) has not a saddle point at (0,0) when a = 0. (Türkçe: a = 0 iken f(x, y), (0,0)'da eyer noktasına sahip değildir.) 8. f(x, y) has not a saddle point at (0,0) for a > 0. (Türkçe: a > 0 için f(x,y),
Let a be a constant and f(x, y) = x³ – 3axy + y³. Determine that the following statements are "True" or "False". Türkçe: (f(x, y) = x³ – 3axy + y³ ve a bir sabit olmak üzere aşağıdaki ifadelerin "Doğru" veya "Yanlış" olduğunu belirleyiniz. ) 1. f(x, y) has a local minimum value at (a, a) for a > 0. (Türkçe: f(x,y) fonksiyonu a > 0 için (a, a)'da yerel minimuma sahiptir.) 2. f(x, y) has a local minimum value at (a, a) for a < 0. (Türkçe: ƒ(x, y) fonksiyonu a < 0 için (a, a)'da yerel minimuma sahiptir.) 3. f(x, y) has a local maximum value at (a, a) for a < 0. (Türkçe: ƒ(x, y) fonksiyonu a < 0 için (a, a)'da yerel maksimum sahiptir.) 4. f(x, y) has a local maximum value at (a, a) for a > 0. (Türkçe: f(x,y) fonksiyonu a > 0 için (a, a)'da yerel maksimum sahiptir.) 5. f(x, y) has a saddle point at (0, 0) when a = 0. (Türkçe: a = 0 iken f(x, y), (0,0)'da eyer noktasına sahiptir.) 6. f(x, y) has a saddle point at (0, 0) for a > 0. (Türkçe: a > 0 için f(x, y), (0, 0)'da eyer noktasına sahiptir.) 7. f(x, y) has not a saddle point at (0,0) when a = 0. (Türkçe: a = 0 iken f(x, y), (0,0)'da eyer noktasına sahip değildir.) 8. f(x, y) has not a saddle point at (0,0) for a > 0. (Türkçe: a > 0 için f(x,y),
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
Related questions
Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
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.Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning