If `f : [-5, 5] to R` is a differentiable function and if `f^(prime)(x)` does not vanish anywhere, then prove that `f(-5) ne f(5)`.

Explanation

It is given that f(x) is a differentiable function , so it is clear that it is also a continous function.

Now let's apply mean value theorem

So as the theorem apply , there exist a c in (5,-5)

Such that `f'(c)=(f(b)-f(a))/(b-a)`

Given that

`f'(x)` does not vanish any where

`rArrf'(x) ne 0` for any value of x

Thus ,

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