Proff of the Numerical Derivative

Click For Summary
SUMMARY

The discussion centers on proving the formula for the numerical derivative, specifically that f´(x) equals the limit as delta x approaches 0 of the expression (f(a + delta x) - f(a - delta x)) / (2 delta x). A participant seeks clarification on how to manipulate the equation to reach the proof, referencing a hint from their textbook to rearrange the terms. The correct approach involves using the limit definition of the derivative and simplifying the expression accordingly.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with the definition of derivatives
  • Basic algebraic manipulation skills
  • Knowledge of Taylor series expansion (optional but helpful)
NEXT STEPS
  • Study the limit definition of the derivative in calculus
  • Learn about Taylor series and their applications in approximating functions
  • Practice algebraic manipulation of limits and derivatives
  • Explore numerical methods for derivative approximation
USEFUL FOR

Students studying calculus, particularly those focusing on derivatives and limits, as well as educators looking for teaching strategies in mathematical proofs.

Jimmy84
Messages
190
Reaction score
0

Homework Statement



Proff that f´(x) = the lim of delta x approaching to 0 of

f (a + delta x) - f (a -delta x) / 2 delta x


Homework Equations





The Attempt at a Solution



the book hinted me that I should solve it in this way


f (a + delta x) - f (a) + f (a) - f (a - delta x) / 2 delta x

but I am stuck here and I don't know how to proff this. I d appreciate some help, thanks a lot in advance.
 
Physics news on Phys.org
The word is prove, not proff.

Anyhow, try it with

[tex]\frac 1 2 \,\frac {f(a+\Delta x) - f(a) \,\,\,+\,\,\, f(a) - f(a-\Delta x)}{\Delta x}[/tex]
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
2
Views
2K
Replies
7
Views
2K