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| PAGE: 212 | SET: Exercises | PROBLEM: 35 |
Critical number :
A critical number of a function 
is a number 
in the domain of such that either 
or 
does not exist.
The function 
.
Solutions of 
and points where 
does not exist are the critical numbers.
Differentiate on each side with respect to 
.
Apply quotient rule in derivatives 
.
.
Find the critical numbers by equating the first derivative to zero.
Apply zero product property.
and 
and 
.
The function 
does not exist when 
.
The discriminant of the above equation: 
.
Since 
, the roots are imaginary.
Hence, they are not considered.
Critical numbers are and .
Critical numbers are and .
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