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If f (x) = x (sqrtx+sqrt((x+1)), then...

If ` f (x) = x (sqrtx+sqrt((x+1))`, then

A

f (x) is continuous but not differentiable at `x=0`

B

f (x) is differentiable at `x=0`

C

f (x) is not differentiable at `x=0`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Given ` f (x ) = x ( sqrt x + sqrt ( x + 1 ) ) `. At ` x = 0 ` LHL of ` sqrt x ` is not defined, therefore it is not continuous at ` x = 0 `.
Hence, it is not differentiate at ` x = 0 `
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