Thread: Absolute Extrema

After deriving f(x) = (x+2)/x, I got -2/(x^2)..

How do I find the absolute extrema if there are no critical numbers?

Originally Posted by AppleTini

After deriving f(x) = (x+2)/x, I got -2/(x^2)..

How do I find the absolute extrema if there are no critical numbers?

In general if there is no critical number, the extrema can be found at the extremities of the interval you consider.

You can see that -2/x² is always negative, whatever x is. Hence the function is strictly decreasing.

So if you consider the interval [1,2], the absolute maximum will be at 1 and the absolute minimum will be at 2.

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Now you should get back to the definition of a critical point. It's a point where the derivative is 0 or a point where the derivative is undefined.
So x=0 is a critical point.

But yes, it doesn't give any extrema.

An absolute minimum can be found by looking at the limit of the function as x goes to infinity. The function will always be "above" this value.