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If f is a continuous function on [0,1], ...

If `f` is a continuous function on `[0,1],` differentiable in (0, 1) such that `f(1)=0,` then there exists some `c in (0,1)` such that `cf^(prime)(c)-f(c)=0` `cf^(prime)(c)+cf(c)=0` `f^(prime)(c)-cf(c)=0` `cf^(prime)(c)+f(c)=0`

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