It is given that if $f^{'} (x) > 0$ for all $x$ in $(a, b)$ , then $f$ has no stationary point in $(a, b)$ . A student concludes: ' $f$ has no stationary point in $(a, b)$ , so $f^{'} (x) > 0$ for all $x$ in $(a, b)$ .' What is wrong with this argument?

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Which of the following arguments is valid?
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