Q3 If is a differentiable function and if does not vanish
anywhere, then prove that
It is given that
is a differentiable function
Now, f is a differential function. So, f is also a continuous function
We obtain the following results
a ) f is continuous in [-5,5]
b ) f is differentiable in (-5,5)
Then, by Mean value theorem we can say that there exist a c in (-5,5) such that
Now, it is given that does not vanish anywhere
Therefore,
Hence proved