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Let $f: R \rightarrow R$ be a differentiable function such that $f(a)=0=f(b)$ and $f^{\prime}\left(\right.$ a) $f^{\prime}(b)>0$ for some $a < b$. Then the minimum number of roots of $f^{\prime}(x=0$ in the interval $(a, b)$ is-
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The correct answer is:
2
$f^{\prime}(a), f^{\prime}(b)>0$
so either both are positive or both are negative
$\mathrm{f}(\mathrm{a})=\mathrm{f}(\mathrm{b})=0$
2 roots
so either both are positive or both are negative
$\mathrm{f}(\mathrm{a})=\mathrm{f}(\mathrm{b})=0$
2 roots
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