Verify Rolles theorem for function `f(x)=sin^4\ x+cos^4\ x` on `[0,\ pi/2]`

Explanation

Solution:
We know that every sine and co-sine functions is continuous and differentiable everywhere.

So, it is continuous on `[0, \pi / 2]`

and differentiable on `(0, \pi / 2)`

Also, `f(0)=1=f(\pi / 2)`

Thus, all the conditions of Rolle's theorem are satisfied.

Now, we have to show that there exist a point c in `(0, \pi / 2)` such that `f^{\prime}(c)=0`

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