AP EAMCET · Maths · Application of Derivatives
If \(f(x)=x^\alpha \log x\) and \(f(0)=0\), then the value of \(\alpha\) for which Rolle's theorem can be applied in \([0,1]\) is
- A -2
- B -1
- C 0
- D \(1 / 2\)
Answer & Solution
Correct Answer
(D) \(1 / 2\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^a \log x\) and \(f(0)=0\) \(\because\) Rolle's theorem is applicable in \([0,1]\). \(\Rightarrow\) It is continuous in closed interval \([0,1]\) and It is differentiable in \((a, b)\) and \(f(0)=f(1)\). \(\because f(x)\) is continuous at \(x=0\)…
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