2. Let f : R³ → R be the function defined as ƒ(x) = x² + x² + x² + 2x2. Accordingly: (a) Write the equation of the vertical surface S₁ = {x € R³ : f(x) = 0} and draw its graph. (b) Compute the gradient vector of f' as “▼ƒ(x) = Dƒ(x)™" and the Hessian matrix as “F(x) = D² f(x)". (c) Find the unit direction in which the decrease of f' is maximal at the point x compute the derivative of the function in that direction. [0 - 1 1] and (d) Find the point satisfying the FONC condition of f' and determine using SOSC whether this point is a local minimizer of f'.
2. Let f : R³ → R be the function defined as ƒ(x) = x² + x² + x² + 2x2. Accordingly: (a) Write the equation of the vertical surface S₁ = {x € R³ : f(x) = 0} and draw its graph. (b) Compute the gradient vector of f' as “▼ƒ(x) = Dƒ(x)™" and the Hessian matrix as “F(x) = D² f(x)". (c) Find the unit direction in which the decrease of f' is maximal at the point x compute the derivative of the function in that direction. [0 - 1 1] and (d) Find the point satisfying the FONC condition of f' and determine using SOSC whether this point is a local minimizer of f'.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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optımızatıon theory
![2. Let f : R³ → R be the function defined as ƒ(x) = x² + x² + x² + 2x2. Accordingly:
(a) Write the equation of the vertical surface S₁ = {x € R³ : f(x) = 0} and draw its graph.
(b) Compute the gradient vector of f' as “▼ƒ(x) = Dƒ(x)™" and the Hessian matrix as “F(x) =
D² f(x)".
(c) Find the unit direction in which the decrease of f' is maximal at the point x
compute the derivative of the function in that direction.
[0
-
1 1] and
(d) Find the point satisfying the FONC condition of f' and determine using SOSC whether this point is a
local minimizer of f'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cd79f82-3730-49d1-8559-a01cc4e6e9ca%2F60c6b426-f039-4d70-8cfe-34f2cdc09a77%2Fjqqa4xg_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let f : R³ → R be the function defined as ƒ(x) = x² + x² + x² + 2x2. Accordingly:
(a) Write the equation of the vertical surface S₁ = {x € R³ : f(x) = 0} and draw its graph.
(b) Compute the gradient vector of f' as “▼ƒ(x) = Dƒ(x)™" and the Hessian matrix as “F(x) =
D² f(x)".
(c) Find the unit direction in which the decrease of f' is maximal at the point x
compute the derivative of the function in that direction.
[0
-
1 1] and
(d) Find the point satisfying the FONC condition of f' and determine using SOSC whether this point is a
local minimizer of f'.
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