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Critical numbers occur where g'(y) equals 0 or is undefined. g'(y) is undefined where the quadratic y2 − 2y + 4 in the denominator is 0. So, g'(y) is undefined for the following values. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

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Answer:

There are no real values of y for which g'(y) is undefined.

Step-by-step explanation:

We are given the following in the question:

[tex]g(y) = y^2 - 2y +4[/tex]

We have to find values for which g'(y) is undefined.

[tex]g'(y) = 2y-2[/tex]

Putting g(y) = 0, we get:

[tex]y^2 - 2y +4 = 0\\y^2 -2y +1+3 = 0\\(y-1)^2=-3\\y-1=\sqrt{-3}\\y-1 = i\sqrt3\\y = 1 \pm i\sqrt3[/tex]

Since those are not real numbers, there are no real numbers where g'(y) is undefined.

Thus, there are no real values of y for which g'(y) is undefined.

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