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A single valued function f(x) of x defin...

A single valued function f(x) of x defined in [a, b] satisfies the following conditions :
(i) f(x) is continuous in [a, b]
(ii) f'(x) exists in (a, b)
(iii) f(a)=f(b)
Then, Rolle's theorem is applicable to f(x), if -

A

(i) and (ii) are satisfied

B

(ii) and (iii) are satisfied

C

(i) and (iii) are satisfied

D

(i), (ii) and (iii) all are satisfied

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • A real valued function f(x) of a real variable x is defined in [a, b] such that, (i) f(x) is continuous in [a, b], (ii) It is differentiable in (a, b), (iii) its second order derivative exists in (a, b), then Lagrange's Mean Value theorem is applicable to f(x) if -

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    C
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    3
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    1
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    2
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  • A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

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