MonotonicityHard

Question

Consider f(x) = l 1 - x l , 1 ≤ x ≤ 2 and g(x) =  f(x) + b sin π/2 x, 1 ≤ x ≤ 2 then which of  the following is correct ?

Options

A.Rolles theorem is applicable to both f, g and b = 3/2
B.LMVT is not applicable to f and Rolles theorem If applicable to g with b = 1/2
C.LMVT is applicable to f and Rolles theorem is applicable to g with b = 1
D.Rolles theorem is not applicable to both f, g for any real b.

Solution

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