Exponential Function: Is Infinity a Minimum?

[Niles]

Homework Statement

Hi all

Is infinity a minimum of the exponential function f(x)=e^x or not? I personally do not think so since it is a limit, but I wanted to ask you guys to be 100% sure.

 

[Mark44]

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.

 

[Niles]

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?

 

[Mark44]

Right, but with regard to your original question, there is no minimum value for e^x. As x --> -infinity, e^x --> 0.