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- (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
- (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$

$f(x) =e^{-x} \;on\; [0,1]$

$f'(x)=e^{-x} <0$ for all $x \in R$

$\therefore \; f'(x)$ is strictly decreasing on $[0,1]$

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