Calculus: Early Transcendentals, Chapter 4, 4.1, Section 4.1, Problem 54

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 interval [0, 3].
f(0)=0
f(1)=1
f(3)=3/7
Evaluate the f(x) values to determine the absolute maximum and absolute minimum.
The absolute maximum occurs at the coordinate (1, 1).
The absolute minimum occurs at the coordinate (0, 0).