Deriving functions relating to condition numbers

Click For Summary
SUMMARY

The discussion focuses on deriving functions related to condition numbers for the functions f_1(x) = x^3 and f_2(x) = thirdrootof(x). The asymptotic relative condition number, KR(f,x), is defined as KR = (x f'(x)) / f(x). Participants clarify that the task involves differentiating the functions rather than deriving them. A reference to a relevant wiki article on condition numbers is provided for further understanding.

PREREQUISITES
  • Understanding of differentiation in calculus
  • Familiarity with condition numbers in numerical analysis
  • Basic knowledge of LaTeX for mathematical expressions
  • Concept of asymptotic analysis
NEXT STEPS
  • Study the differentiation of polynomial functions, specifically f_1(x) = x^3
  • Research the properties of the cube root function, f_2(x) = thirdrootof(x)
  • Learn about the implications of condition numbers in numerical stability
  • Explore the section on "One variable" in the Wikipedia article on condition numbers
USEFUL FOR

Students in mathematics or engineering, particularly those studying numerical analysis and optimization, will benefit from this discussion.

mabelw
Messages
1
Reaction score
0
I have a question stating to derive the functions x |-> f_1(x)=x^3 and f_2(x)=thirdrootof(x) on their domains of definition based on the asymptotic relative condition number KR = KR(f,x). I'm not sure where to start with this question, I'm not sure if I even understand it. Do I find the condition number for each of the functions?
 
Physics news on Phys.org
I moved your post from the Homework section you started it in. Be advised that homework questions must use the homework template that you deleted.

Your functions are ##f_1(x) = x^3## and ##f_2(x) = \sqrt[3]{x}##. Rightclick on either of the expressions I wrote to see the LaTeX script I used.
This wiki article discusses condition numbers -- https://en.wikipedia.org/wiki/Condition_number -- see the section titled "One variable." The condition number for a nonlinear function is ##\frac {x f'(x)}{f(x)}##, so you will need to differentiate your two functions, not derive them.
 

Similar threads

Graduate Is the functional derivative a function or a functional
  • · Replies 4 ·
Replies
4
Views
3K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Differentiability of a Multivariable function
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Second derivative of chained function
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
High School Functions which relate to calculus: Questions about Notation
  • · Replies 36 ·
2
Replies
36
Views
6K
High School Question about the fundamental theorem of calculus
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How to Find the Derivative of F = f(x)/f(x+dx)?
  • · Replies 15 ·
Replies
15
Views
2K
High School Second Derivative Question -- Help Understanding the Importance Please
  • · Replies 13 ·
Replies
13
Views
3K