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...
(The entire section contains 2 answers and 245 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.