Question: Show that the derivative of f(x) = (x-a)(adsbygoogle = window.adsbygoogle || []).push({}); ^{m}(x-b)^{n}vanishes at some point between a and b if m and n are positive integers.

My attempt:

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

f '(x) = m(x-a)^{m-1}(x-b)^{n}+ n(x-a)^{m}(x-b)^{n-1}

f '(x) = [(x-a)^{n-1}(x-b)^{n-1}] [(m)(x-b) +(n)(x-a)]

And this is as far as I got.

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# Calculus derivative of given function vanishes at some point between a and b

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