Verify Rolles theorem for the function `f(x)=sqrt(4-x^2)` on `[-2,\ 2]` .

Explanation

Given, `f(x)=sqrt(4-x^2)` is a polynomial function which is
continuous in `[-2,2]` and differentiable everywhere except `x=pm 2`. Derivative of Function becomes non defined at `x=pm 2`


`f'(x)=(-x)/(sqrt(4-x^2)`


`f(-2)=sqrt(4-(-2)^2)=0`


`f(2)=sqrt(4-2^2)=0`


`f(-2)=f(2)=0`


All condition of Rolle's theorem is satisfied and so there exist `c in (-2,2)` such that `f'(c)=0`


`f'(x)=(-x)/(sqrt(4-x^2)`


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