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-

• A

  3
• Correct answer
  B

  2
• C

  1
• D

  0

Solution

$f^{\prime}(a), f^{\prime}(b)>0$ so either both are positive or both are negative $\mathrm{f}(\mathrm{a})=\mathrm{f}(\mathrm{b})=0$
2 roots

Hence, the correct answer is option: 'B'.