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If f(x)= (x-1)/(2x^2-7x+5) for x!=1 and ...

If `f(x)= (x-1)/(2x^2-7x+5)` for `x!=1` and `f(x)=-1/3` for `x=1` then `f'(1)=`

A

`-1/9`

B

`-2/9`

C

`-13`

D

`1//3`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(1) = underset( h to 0) lim (f(1 + h) - f(1))/(h)`
`=underset(h to 0)lim((1+h-1)/(2(1 + h)^(2) - 7(1 + h) + 5) - (-(1)/(3)))/(h)`
`=underset(h to 0)lim(((1)/(2h-3) + (1)/(3)))/(h) =underset(h to 0)lim((2h)/(3h (2h-3))) = - (2)/(9)`
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