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If f(x)=x^3-x^2+100x+2002 ,t h e n f(1...

If `f(x)=x^3-x^2+100x+2002 ,t h e n` `f(1000)>f(1001)` `f(1/(2000))>f(1/(2001))` `f(x-1)>f(x-2)` `f(2x-3)>f(2x)`

A

`f(1000)ltf(1001)`

B

`f((1)/(2000))gtf((1)/(2001))`

C

`f(x-1)gtf(x-2)`

D

`f(2x-3)gtf(2x)`

Text Solution

Verified by Experts

The correct Answer is:
2,3
`f(X)=x^(3)-x^(2)+100x+2002`
`f(x)=3x^(2)-2x+100gt0 forall x in R` thus
Therefore fX() is increasing (strictly) Thus
`f((1)/(2000))gtf((1)/(2001))`
Also `f(X-1)gtf(x-2)asx-1gtx-2forallx`
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