Question

verify rolles theorem​

Answer 1

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Answer 2

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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