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Suppose $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$. If $f'(x)>0$ for every $x\in(a,b)$, then $f$ is
Astrictly increasing on $[a,b]$
Bstrictly decreasing on $[a,b]$
Cconstant on $[a,b]$
Dnot necessarily monotonic
Answer & Solution
Correct answer: A. strictly increasing on $[a,b]$
A positive derivative throughout an interval implies that the function increases as $x$ increases. Therefore $f$ is strictly increasing on the interval. A negative derivative would imply strict decrease.
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