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If f"(x) exists for all points in [a,b] ...

If f"(x) exists for all points in `[a,b]` and
`(f(c )-f(a))/(c-a)=(f(b)-f( c))/(b-c),"where"a lt clt b,` then show that there exists a number 'k' such that f"(k)=0.

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