`f(x) = x/(x^2 - x + 1), [0, 3]` Find the absolute maximum and minimum values of f on the given interval

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Given: `f(x)=x/(x^2-x+1), [0,3].`

Find the critical values by setting the first derivative equal to zero and solving for the x values. Find the derivative using the quotient rule.

`f'(x)=[(x^2-x+1)(1)-x(2x-1)]/(x^2-x+1)^2=0`

`x^2-x+1-2x^2+x=0`

`-x^2+1=0`

`x^2=1`

`x=+-sqrt(1)`

`x=+-1` 

The critical values are x=1 and x=-1. Substitute the critical values and the endpoints of the interval [0, 3] in to the original f(x) function. Do NOT substitute in the x=-1 because it is not in the given...

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