Question

Correct option (D) ( 1 / 2 )
Explanation:
For Function to satisfy the
condition of Rolle's theorem, it
should be continuous in [0,1]
( Rightarrow lim _{x rightarrow 0^{+}} f(x)=f(0) )
( Rightarrow lim _{x rightarrow 0^{+}} frac{log x}{x^{-alpha}}=0 )
( Rightarrow lim _{x rightarrow 0^{+}} frac{1 / x}{-x x^{-alpha-1}}=0 Rightarrow alpha>0 )
Also ( forall alpha>0, ) f ( (mathrm{x}) ) is differentiable in
(0,1) and ( mathrm{f}(1)=0=mathrm{f}(0) )

# If f(x) = xºlogx and f(0) = 0, then the value of a for which Rolle's theorem can be applied in [0, 1] is 22 b. 1 hod. 1/2 2

Solution