- #1

gruba

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## Homework Statement

Let [itex]f[/itex] is differentiable function on [itex][0,1][/itex] and [itex]f^{'}(0)=1,f^{'}(1)=0[/itex]. Prove that [itex]\exists c\in(0,1) : f^{'}(c)=f(c)[/itex].

## Homework Equations

-Mean Value Theorem

## The Attempt at a Solution

The given statement is not true. Counter-example is [itex]f(x)=\frac{2}{\pi}\sin\frac{\pi}{2}x+10[/itex].

Does this mean that the statement can't be proved?