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Let f(x) =int0^1|x-t|t dt, then A. f(x...

Let `f(x) =int_0^1|x-t|t dt`, then

A. f(x) is continuous but not differentiable for all `x in R`
B. f(x) is continuous and differentiable for all `x in R`
C. f(x) is continuous for `x in R-{(1)/(2)} and f(x)` is differentiable for `x in R - {(1)/(4),(1)/(2)}`
D. None of these

A

f(x) is continuous but not differentiable for all `x in R`

B

f(x) is continuous and differentiable for all `x in R`

C

f(x) is continuous for `x in R-{(1)/(2)} and f(x)` is differentiable for `x in R - {(1)/(4),(1)/(2)}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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