`f(x) = 2/(2 - x), [0,2)` Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval.

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gsarora17 eNotes educator| Certified Educator

`f(x)=2/(2-x)`

Now to find the absolute extrema of the function , that is continuous on a closed interval, we have to find the critical numbers that are in the interval and evaluate the function at the endpoints and at the critical numbers and to find the critical numbers, solve for x for f'(x)=0.

`f'(x)=2(-1)(2-x)^-2(-1)`

`f'(x)=2/(2-x)^2`

`2/(2-x)^2=0`

So x has no solution.

`f(0)=2/(2-0)=1`

So , the function has no Absolute maximum.

Absolute minimum=1 at x=0