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The differentiable function y= f(x) has ...

The differentiable function `y= f(x)` has a property that the chord joining any two points `A (x _(1), f (x_(1)) and B (x_(2), f (x _(2)))` always intersects y-axis at `(0,2 x _(1)x _(2)).` Given that `f (1) =-1.` then:
In which of the following intervals, the Rolle's theorem is applicable to the function `F (x) =f (x) + x` ? (a) `[-1,0]` (b) `[0,1]` (c) `[-1,1]` (d) `[0,2]`

A

`0-1,0]`

B

`[0,1]`

C

`[-1,1]`

D

`[0,2]`

Text Solution

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The correct Answer is:
B
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