Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian is v² f(x) = VxER".

a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian is v² f(x) = VxER".

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
See similar textbooks
icon
Related questions
Question
100%

Which of the following statements are true?

 

a. The function f: R→R given by f(x)=12||x||² is twice continuously differentiable in R", and its Hessian is exists. In this case, we write c. Every differentiable function is a polynomial. Od. We say that a function f: R→R is differentiable at x in R if there exists a in R such that Of. b. We say that a function f: R→R is differentiable at x in R if for every sequence (xk) in R with limk-ooXk-X and xk*x for all k in N, the limit f(xk) - f(x) xk x In this case, we write f'(x)=a. ☐e. We say that a function f: R→R is differentiable at x in R if the limit exists. In this case, we write v² f(x) = The function f: R→R given by f(x)=½||x||2 is continuously differentiable in R", and its gradient is lim k→∞o lim 0#h→0 |h| 3 f'(x) = lim lim 0#h→0 ⠀ VxER". -\f(x +h) − f(x) – ah| = 0. f(xk) - f(x) k→∞o Χk - X f'(x) = lim 0#h→0 f(x +h)-f(x) h f(x+h)-f(x) h Vf(x)=xVxER".
Transcribed Image Text:a. The function f: R→R given by f(x)=12||x||² is twice continuously differentiable in R", and its Hessian is exists. In this case, we write c. Every differentiable function is a polynomial. Od. We say that a function f: R→R is differentiable at x in R if there exists a in R such that Of. b. We say that a function f: R→R is differentiable at x in R if for every sequence (xk) in R with limk-ooXk-X and xk*x for all k in N, the limit f(xk) - f(x) xk x In this case, we write f'(x)=a. ☐e. We say that a function f: R→R is differentiable at x in R if the limit exists. In this case, we write v² f(x) = The function f: R→R given by f(x)=½||x||2 is continuously differentiable in R", and its gradient is lim k→∞o lim 0#h→0 |h| 3 f'(x) = lim lim 0#h→0 ⠀ VxER". -\f(x +h) − f(x) – ah| = 0. f(xk) - f(x) k→∞o Χk - X f'(x) = lim 0#h→0 f(x +h)-f(x) h f(x+h)-f(x) h Vf(x)=xVxER".
Expert Solution
steps

Step by step

Solved in 3 steps

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
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS