Find the critical numbers of the function. g(y)=(y-5)/(y^2-3y+15)

critical-numbers

#1

find the critical numbers of the function. g(y)=(y-5)/(y^2-3y+15)

Answer:

Critical numbers exist when g’(y) = 0 or g’(y) is undefined. g’(y) = [(y^2-3y+15) - (y-5)(2y-3)]/(y^2-3y+15)^2 = (-y^2+10y)/(y^2-3y+15). g’(y) = 0 when -y^2+10y = 0. Hence, y = 0, 10. g’(y) is undefined when (y^2-3y+15)^2 = 0 but this does not occur for any y values.
Therefore, the critical numbers for g(y) occur when y = 0, 10.