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If f(x)=(x-1)(x-2)(x-3), x in [1,3], the...

If `f(x)=(x-1)(x-2)(x-3), x in [1,3]`, then

A

Rolle's theorem is satisfied in [1,3]

B

Rolle's theorem is satisfied in [1,3]

C

`f(1) ne f(3)`

D

`f(1) = f(3)=2`

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The correct Answer is:
A
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NIKITA PUBLICATION-APPLICATIONS OF DERIVATIVES-MULTIPLE CHOICE QUESTIONS
  1. If f(x)=2(x-1)^(2), x in [0,2] then Rolle's theorem satisfies at

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  2. If f(x)=(x-1)(2x-3), x in [1,3], then

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  3. If f(x)=(x-1)(x-2)(x-3), x in [1,3], then

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  4. If f(x)=x^((2)/(3)), x in [-1,1], then

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  5. If f(x)=|x|, x in [-2,2], then

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  6. If f(x) = x^3 + bx^2 + ax satisfies the conditions on Rolle's theorem ...

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  7. If the functio f(x)^(3)-6x^(2)+ax+b satisfies Rolle's theorem in the i...

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  8. Verify Rolle's theorem for the following functions f(x) = sin x + cos ...

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  9. If f(x)=e^(x) sin x, x in [0, pi], then

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  10. A function f is defined by f(x)=x^(x) sin x in [0,pi]. Which of the fo...

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  11. If the Rolle's theorem for f(x)=e^(x)(sin x-cosx) is verified on [(pi)...

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  12. Verify Rolle's theorem for each of the following functions : f(x) = ...

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  13. If Rolle's theorem holds for the function f(x) = (x - 2) log x, x in [...

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  14. If Rolle's theorem holds for the function f(x) = (x - 2) log x, x in [...

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  15. The equation x log x = 3-x has, in the interval (1,3) :

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  16. Verify LMVT for the following function f(x)=x^2-3x-1, x in[-11/7, 13/7...

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  17. Verify LMVT for the following functions: f(x)=x(2-x), x in [0, 1]

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  18. If LMVT is applicable for f(x)=x(x+4)^(2), x in [0,4], then c=

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  19. Find c if LMVT is applicable for f(x)=x(x-1)(x-2), x in [0, 1 /2]

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  20. If mean value theorem holds for the function f(x)=(x-1)(x-2)(x-3), x i...

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