Answer:
For
(i) and (ii), f(x) is an greatest integer function which is not continuous at
integral points belong to given corresponding intervals.
Since
f(x) does not satisfy all the conditions of L.M.V. theorem, therefore L.M.V.
theorem is not applicable for these functions.
(iii)
f(x) = x2 ? 1 in [1, 2]
(a) f(x) is a polynomial
function
is continuous
in [1, 2]
(b) f?(x) exists
uniquely in (1, 2)
is
derivable in (1, 2)
Since f(x) satisfies
all the conditions of L.M.V. theorem
Therefore L.M.V.
theorem is valid for this function and so there exists at least one .
Such that f?(c)
Hence the theorem
is verified.
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