Ononot — Let f be continuous on [0, 1] and differentiable on (0, 1).

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Limits & Continuityhard

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Let $f$ be continuous on $[0, 1]$ and differentiable on $(0, 1)$ . If $f(0) = 0$ and $f'(x) \geq 1$ , what is the minimum value of $f(1)$ ?