InterviewSolution
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InterviewSolution
| 1. |
Let S be the set of all functions f : [0, 1] →R which are continuous on [0, 1] and differentiable on (0, 1). Then for every f in S. there exists a c ∈ (0, 1). depending on f, such that(1) |f(c) - f(1)| < (1 - c)|f'(c)|(2) |f(c) - f(1)| < |f'(c)|(3) |f(c) + f(1)| < (1 + c)| f'(c)|(4) (f(1) - f(c))/(1 - c) = f'(c) |
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Answer» Option (1), (2), (3) are incorrect for ƒ(x) = constant and option (4) is incorrect (f(1) - f(c))/(1 - c) = f'(a) where c < a < 1 (use LMVT) Also for f(x) = x2 option (4) is incorrect. The correct option is (3) |f(c) + f(1)| < (1 + c)| f'(c)| Use LMVT theorem & check option. |
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