Aspire Faculty ID #18392 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

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

Solution

For continuity at $x=0$, need $\lim_{x\to 0^+} x^\alpha \log x = 0$ This holds when $\alpha > 0$ is not satisfied here, but by given condition extension works only at $\alpha = -1$
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