Analyze two variable function with respect to another function

  • Context: Undergrad 
  • Thread starter Thread starter Essa1987
  • Start date Start date
  • Tags Tags
    Function Variable
Click For Summary
SUMMARY

The discussion centers on analyzing the function f(x,y) = (a-bx)^2 - (c-dy)^2 with respect to the variable change (x-y). Participants suggest transforming the function into g(u,v) using the substitutions u = x-y and v = x+y. The derivative ∂g/∂u is proposed as a method to understand how f changes with respect to u. However, the ambiguity in choosing the variable v, such as using v = x instead of v = x+y, indicates that multiple approaches can yield different results.

PREREQUISITES
  • Understanding of multivariable calculus
  • Familiarity with partial derivatives
  • Knowledge of function transformations
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the concept of partial derivatives in depth
  • Learn about function transformations in multivariable calculus
  • Explore the implications of variable substitution in calculus
  • Investigate different methods for analyzing function behavior with respect to variable changes
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on calculus and function analysis, as well as educators seeking to clarify concepts related to multivariable functions.

Essa1987
Messages
2
Reaction score
0
Can you please help me with the following problem:
Given a function of the form f(x,y) = (a-b x)^2 - (c - d y)^2, how can I tell how does f change when (x-y) change?
 
Physics news on Phys.org
I am not quite sure what they question is supposed to represent. However, let u = x-y and v = x+y, then change f(x,y) into g(u,v). I believe that the answer would be ∂g/∂u.

The ambiguity is that v = x+y is not the only choice possible.
 
Thank you, mathman!

I agree, I was thinking about the ambiguity as well. I could also choose v = x etc and this will lead to a different solution.

I do not understand, however, what else do I need to know about the problem to make it concrete?
 

Similar threads

Undergrad Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad ##f(2x)=f^2(x)-2f(x)-1/2## then find ##f(3)##
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad How to manipulate functions that are not explicitly given?
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Change of variables clarification
  • · Replies 5 ·
Replies
5
Views
2K
High School Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Approximation of a function of two variables
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad An attempt to find the total differential of a two-variable function
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Lipschitz continuity of vector-valued function
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Inverse Functions: x=f(y) and X=f^-1(y)
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding minimum value of function with two variable
  • · Replies 7 ·
Replies
7
Views
3K