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If f:[0,1]rarrR is defined as f(x)={(x^(...

If `f:[0,1]rarrR` is defined as `f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1),(0 x=0):}`, then

A

`f` is continuous in `[0,1]`

B

`f` is differentiable in `[0,1]`

C

`f` is discontinuous in `[0,1]`

D

`f` is not differentiable in `[0,1]`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`f^(')(0^(+))=lim_(hrarr0^(+))((h^(3)(1-h)sin1/(h^(2))-0)/h)=0`
Hence `f` is differentiable in `[0,1]`
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