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Q.

Statement I : If Rolle’s theorem be applied in f(x) then Lagrange’s Mean Value theorem(LMVT) is also applied in f(x)
Statement II : Both Rolle’s theorem and LMVT cannot be applied in f(x)=|sin|x||   in[π4,π4]

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a

Statement-I and Statement-II are true Statement-II is the correct explanation of Statement-I

b

Statement-I and Statement-II are true Statement-II is not the correct explanation of Statement-I

c

Statement-I is true but Statement-II is false

d

Statement-I is false but Statement-II is true

answer is B.

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Detailed Solution

For Rolle’s theorem and LMVT, f(x) must be continuous in [a,b] and differentiable in  (a,b). Hence, Statement-I is true. Since f(x)=|sin|x||   in[π4,π4] is non-differentiable at x=0. Hence Statement-II is also  true.

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Statement I : If Rolle’s theorem be applied in f(x) then Lagrange’s Mean Value theorem(LMVT) is also applied in f(x)Statement II : Both Rolle’s theorem and LMVT cannot be applied in f(x)=|sin|x||   in[−π4,π4]