`f(x) = 3/(x - 1), (1,4]` Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval.

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Chapter 3, 3.1 - Problem 41 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`f(x)=3/(x-1)`

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.

`f'(x)=3(-1)(x-1)^-2`

`f'(x)=-3/(x-1)^2`

Now to find the critical numbers, solve for x for f'(x)=0.

`-3/(x-1)^2=0`

So , x has no solution

`f(4)=3/(4-1)=1`

So the function has no Absolute Maximum

Absolute minimum = 1 at x=4.

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