Verify Rolles theorem for the function `f(x)=(x-a)^m(x-b)^n` on the interval `[a ,\ b]` , where `m ,\ n` are positive integers.

Explanation

Given` f(x)=(x-a)^{m}(x-b)^{n}`

As we know that every polynomial function is continuous and differentiable everywhere.


So, `f(x)` is continuous and differentiable on the given indicated interval.


Also, `f(a)=0=f(b).`


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