   Chapter 3.1, Problem 35E

Chapter
Section
Textbook Problem

# Find the critical numbers of the function. g ( y ) = y − 1 y 2 − y + 1

To determine

To find:

The critical numbers of the given function.

Explanation

1) Concept:

Differentiate g(y) with respect to y, and then find the values of y where g'y=0 and g'y doesn’t exist. That gives the critical numbers.

2) Definition:

A critical number of a function f   is a number c in the domain of f  such that either  f'c=0 or f'c does not exist.

3) Given:

gy=y-1y2-y+1

4) Calculation:

Differentiate g(y) with respect to y by using the quotient rule of derivative:

g'y=y2-y+1ddyy-1-y-1ddy(y2-y+1)y2-y+12

g'y=y2-y+1-(y-1)(2y-1)y2-y+12

g'y=y2-y+1-(2y2-3y+1)y2-y</

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