﻿ If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is: : Kaysons Education

# If f (x) = xα log x and f (0) = 0, Then The Value Of ‘α’ For Which Rolle’s Theorem Can Be Applied In [0, 1] Is:

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## Question

### Solution

Correct option is

1/2

Clearly f (x) is continuous and differentiable on (0, 1) for α > 0.

Also, f (0) = 0 = (1)

For f (x) to be continuous at x = 0, we must have

So, f (x) is continuous at x = 0 for α > 0.

∴ By Rolle’s theorem can be applied on f (x) in [0, 1] for all α > 0

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