Find the critical numbers of the function.

Question

g(y) = (y - 1 ) / (y^2 - y +1)

Answer 1

Step 1:

The function

differentiate on each side with respect to .

Apply Quotient rule in derivatives .

.

Step 2:

Find the critical numbers by equate the first derivative to zero.

The function does not exist when .

The discriminant of the above equation .

Since the roots are imaginary.

The denominator does not have real roots.

Equate the numerator of to zero.

Apply zero product property.

and

Critical numbers are and .

Solution:

Critical numbers are and .