Math CentralQuandaries & Queries


Question from kemelo, a student:

show for the following function f(x)=x+1/x has its min value greater than its max value


The maximum and minimum are relative extrema.

To understand the problem I would sketch a diagram. You probably have an app on your computer that will graph the function. Here is what Grapher produced on my Mac.


Graph of y = x + 1/x

You can see that the graph indicates a relative minimum near $x = 1,$ a relative maximum near $x = -1$ and the relative maximum is less than the relative minimum. Can you use calculus now to verify that this is true?




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