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If f(x)=[x], where [x] is the greatest i...

If `f(x)=[x]`, where [x] is the greatest integer not greater than x, then f'(`1^(+)`)= . . .

A

1

B

2

C

0

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
We have , `f(x) = [x]`
`therefore f(1^(+)) = underset(x to 1^(+)) (lim)(f(x) -f(1))/(x-1) = underset(h to 0)(lim) (f(1+h) -f(1))/(h)`
`= underset(lim) ([1+h] -[1])/(h) rArr underset(hto 0)(lim) (1-1)/(h) = 0`
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