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The value of c in Rolle's theorem for t...

The value of `c` in Rolle's theorem for the function `f(x) = x^(3) - 3x` in the interval `[0,sqrt(3)]` is

A

`1`

B

`-1`

C

`3/2`

D

`1/3`

Text Solution

Verified by Experts

The correct Answer is:
A
`:' f'(c ) = 0` , `[:' f'(x) = 3x^(2)-3]`
`rArr 3c^(2)-3=0`
`rArr c^(2) = 3/3 = 1`
`rArr c = +- 1`, where `1 in (0, sqrt(3))`
` :. c = 1`
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
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  6. Derivative of x^(2) w.r.t. x^(3) is

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  7. If f(x) = |cosx|, then f'(pi/4) is equal to "……."

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  8. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is 1//2 (...

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  9. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

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  10. If f is continuous on its domain D; then |f| is also continuous on D

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  11. If f is continuous on its domain D; then |f| is also continuous on D

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  12. The composition of two continuous function is a continuous function.

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  13. Trigonometric and inverse trigonometric functions are differentiable ...

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  14. If f.g is continuous at x = 0 , then f and g are separately continuou...

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  15. Examine contnuity of the function f(x) = x^(3) + 2x^(2)- 1 at x = 1.

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  16. f(x)={{:(3x+5, if x ge 2),(x^(3), if x le 2):}at x = 2

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  17. f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0.

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  18. f(x) = {{:((2x^(2)-3x-2)/(x-2), if x ne 2), (5, if x = 2):} at x = 2.

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  19. f(x)= {{:((|x-4|)/(2(x-4)), if x ne 4),(0,if x = 4):} at x = 4.

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  20. f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if x =0):} at x = 0 .

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