Q2 (2) Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?
According to Rolle's theorem function must be
a ) continuous in given closed interval say [x,y]
b ) differentiable in given open interval say (x,y)
c ) f(x) = f(y)
Then their exist a such that
If all these conditions are satisfies then we can verify Rolle's theorem
Given function is
It is clear that Given function is not continuous for each and every point in [-2,2]
Now, lets check differentiability of f(x)
L.H.L. at x = n ,
R.H.L. at x = n ,
We can clearly see that R.H.L. is not equal to L.H.L.
Therefore, function is not differential in (-2,2)
Hence, Rolle's theorem is not applicable for given function ,