Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval, and indicate the x-values at which they occur.
f(x) = x
3 - x
2 - x + 5; [0, 2]
![](data:image/png;base64, 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)
◦ Absolute maximum = 7 at x = 2; absolute minimum = 5.2 at x = 0
◦ Absolute maximum = 5.2 at x = 2; absolute minimum = 4 at x = 0
◦ Absolute maximum = 7 at x = 2; absolute minimum = 4 at x = 1
◦ Absolute maximum = 5 at x = 0; absolute minimum = 4 at x = 1