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| PAGE: 174 | SET: Exercises | PROBLEM: 1 |
The function is 
and the interval is 
.
Rolle
s Theorem :
Let 
be a function that satisfies the following three hypotheses.
1. is continuous on 
.
2. is differentiable on 
.
3. 
.
Then there is a number 
in such that 
.
The function is .
Substitute 
in .
.
Substitute 
in .
.
.
The function is 
and the interval is .
A function is continuous when, for every value in its domain, 
is defined, and 
.
Consider the number as 
.
.
Since the function is undefined at 
, it is discontinuous on the interval .
Since the function is discontinuous on the interval 
, it does not satisfies the Rolle
s Theorem.
.
The function is discontinuous on the interval , it does not satisfies the Rolles Theorem.
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