Question

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.)

Answer 1

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

Explanation:

We are given the following in the question:

`g(y) = y^2 - 2y +4`

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

`g'(y) = 2y-2`

Putting g(y) = 0, we get:

`y^2 - 2y +4 = 0\\y^2 -2y +1+3 = 0\\(y-1)^2=-3\\y-1=√(-3)\\y-1 = i\sqrt3\\y = 1 \pm i\sqrt3`

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.