verify rolles theorem
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STATEMENT OF ROLLES THEOREM IS
1) Function should be Continuous on Closed intervel.
2) Function should be differentiable on
Open intervel.
3) End point values must be same
If these 3 conditions are satisfied then their exists some value c such that
F' ( c ) = 0 c lies between given intervel.
_______________________________
Exp:-
The given functions is both continuous and differentiable on ( 0, π/2 )
F ( 0 ) =0 And F ( π/2 ) = 0
F' ( c ) = Cos x - Sin x
Cos x = Sin x
Tan x = 1
x = π/4
x€ ( 0 , π/2 )
Hence, ROLLES THEOREM IS VERIFIED
STATEMENT OF ROLLES THEOREM IS
1) Function should be Continuous on Closed intervel.
2) Function should be differentiable on
Open intervel.
3) End point values must be same
If these 3 conditions are satisfied then their exists some value c such that
F' ( c ) = 0 c lies between given intervel.
_______________________________
Exp:-
The given functions is both continuous and differentiable on ( 0, π/2 )
F ( 0 ) =0 And F ( π/2 ) = 0
F' ( c ) = Cos x - Sin x
Cos x = Sin x
Tan x = 1
x = π/4
x€ ( 0 , π/2 )
Hence, ROLLES THEOREM IS VERIFIED
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