# Never expected Rolle's

Calculus Level 3

Let $$f(x)$$ be a continuous and differentiable function on $$[0,1]$$, such that $$f(0)\ne0$$ and $$f(1)=0$$. We can conclude that there exists $$c\in (0,1)$$ such that

$cf'(c)+f(c)=k$

What is the value of $$k$$?

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