Question

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

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

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) )