Exponential Function: Is Infinity a Minimum?

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Homework Help Overview

The discussion revolves around the properties of the exponential function f(x) = e^x, specifically whether infinity or negative infinity can be considered a minimum value of the function.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the nature of infinity in relation to the minimum value of the exponential function, expressing uncertainty about its classification. Other participants clarify that infinity is not a number in the real number system and discuss the implications for minimum values.

Discussion Status

Participants are exploring the concept of minimum values in the context of the exponential function, with some clarifying that there is no minimum value for e^x as x approaches negative infinity. The discussion is ongoing, with different interpretations being considered.

Contextual Notes

There is a focus on the definitions and properties of infinity within the real number system, as well as the implications for the function's behavior at extreme values.

Niles
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Homework Statement


Hi all

Is infinity a minimum of the exponential function f(x)=ex or not? I personally do not think so since it is a limit, but I wanted to ask you guys to be 100% sure.
 
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You probably meant maximum, not minimum. Since infinity is not considered to be a number in the real number system, e^x does not have a maximum value.
 
Ahh, I meant minus infinity (-inf). Sorry, my bad. But I guess that -inf is not considered a number in the real number system as well, so it is not a minimum?
 
Right, but with regard to your original question, there is no minimum value for e^x. As x --> -infinity, e^x --> 0.
 

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