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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), g (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 9x) =f (x) + x` ?

A

`0-1,0]`

B

`[0,1]`

C

`[-1,1]`

D

`[0,2]`

Text Solution

Verified by Experts

The correct Answer is:
B
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VK JAISWAL-APPLICATION OF DERIVATIVES -EXERCISE (COMPREHENSION TYPE PROBLEMS)
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  2. Let y = f (x) such that xy = x+y +1, x in R-{1} and g (x) =x f (x) ...

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  3. Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int(...

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  4. Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int(...

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  6. Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f ...

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  7. Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f ...

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  8. Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (...

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