Find the critical numbers of the function.

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SUMMARY

The critical numbers of the function g(y) = (y-1)/(y²-y+1) are identified as y1 = 0 and y2 = 2. The derivative g'(y) is calculated as g'(y) = [y(y-2)]/(y²-y+1)². The denominator (y²-y+1)² does not yield any solutions since it is always positive, confirming that the critical points arise solely from the numerator. A minor correction regarding a missing minus sign in the derivative is noted, but the critical numbers remain valid.

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phillyolly
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Homework Statement



g(y)=(y-1)/(y2-y+1)


Homework Equations





The Attempt at a Solution



After I take a derivative, I get
g'(y)=[y(y-2)]/(y2-y+1)2

However,
(y2-y+1)2 does not have any solutions. Am I right that I just throw it away? As an answer, I only leave
y1=0, y2=2

Is that correct?
 
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phillyolly said:

Homework Statement



g(y)=(y-1)/(y2-y+1)


Homework Equations





The Attempt at a Solution



After I take a derivative, I get
g'(y)=[y(y-2)]/(y2-y+1)2

However,
(y2-y+1)2 does not have any solutions. Am I right that I just throw it away? As an answer, I only leave
y1=0, y2=2

Is that correct?

I wouldn't say "throw it away". I would just observe that the denominator is always positive. And I think you have a minus sign missing but your critical numbers are correct.
 

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