Can a Function Equal Zero with Non-Zero and Unknown?

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Discussion Overview

The discussion revolves around the conditions under which a rational function can equal zero, specifically focusing on the relationship between the numerator and denominator. The scope includes mathematical reasoning and conceptual clarification regarding functions and derivatives.

Discussion Character

  • Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant questions whether a function can equal zero if it has a non-zero numerator and an unknown denominator.
  • Another participant asserts that a rational fraction can only equal zero if the numerator is zero.
  • A later reply connects this idea to derivatives, suggesting that if the numerator becomes zero, there would be no critical points.
  • Another participant agrees with this connection regarding critical points.

Areas of Agreement / Disagreement

Participants generally agree that a rational function can only equal zero if the numerator is zero, but the implications for critical points are discussed without full consensus on the broader context.

Contextual Notes

The discussion does not fully explore the implications of having an unknown denominator or the conditions under which critical points are defined.

Who May Find This Useful

Readers interested in mathematical functions, rational expressions, and calculus concepts may find this discussion relevant.

Femme_physics
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If I have a non-zero on top, and an unknown at the bottom, can this function = 0?
 
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No, a rational fraction can only be zero if the numerator becomes zero...
 
Aha! So if that happens with derivatives, there are no critical points, right?
 
Right!
 
Math is groovy :)

Thanks!
 

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