Is f'(2) the Same as f(2)?

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Discussion Overview

The discussion centers around the relationship between the notation f'(2) and f(2), specifically whether they represent the same value. The scope includes conceptual clarification of derivatives and function evaluation.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants assert that f'(2) refers to the derivative of the function f evaluated at the point 2.
  • Others clarify that f(2) represents the value of the function f at x=2, indicating a distinction between the two notations.
  • One participant provides the definition of the derivative using the limit definition, suggesting a formal approach to understanding f'(2).
  • Another participant emphasizes that f' is a function representing the derivative of f, and f'(2) is the result of evaluating this derivative function at 2.

Areas of Agreement / Disagreement

Participants generally agree that f'(2) and f(2) are not the same, but the discussion includes varying explanations and interpretations of what each notation signifies.

Contextual Notes

Some assumptions about the definitions of functions and derivatives are present, but these are not explicitly stated or resolved in the discussion.

afcwestwarrior
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is it the same as f(2)
 
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No. It usually means the derivative of f evaluated at 2.
 
[tex]f'(2) = \lim_{h \rightarrow 0} \frac{f(2+h) - f(2)}{h}[/tex]
 
thanks man
 
one is height of graph at x=2, one is slope of graph at x=2.
 
f is a function.

f' is a function: it's the derivative of f.

f'(2) is the result of plugging 2 into the function f'
 

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