Verify Rolles theorem for function `f(x)=4^(sinx)` on `[0,\ pi]`

Explanation

We know, `sin` functions are continuous and differentiable on all values of `x`


`f(0)=4^(sin 0)=4^0=1`


`f(pi)=4^(sin pi)=4^0=1`


`f(0)=f(pi)`


There must be `c in (0, pi)` such that `f'(c)=0`


`f'(x)=4^(sin x) *cos x *log 4`


`f'(c)=0`


`f'(c)=4^(sin c) *cos c *log 4=0`


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