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For the fucntion f(x)=x cos ""1/x, x ge ...

For the fucntion `f(x)=x cos ""1/x, x ge 1 `which one of the following is incorrect ? (a)for atleast one x in the interval `[1, oo), f(x + 2) - f(x) lt 2` (b)`underset(x rarr oo)(lim) f'(x) = 1` (c)for all x in the interval `[1, oo), f(x+2) - f(x) gt 2` (d)f'(x) is strictly decreasing in the interval `[1, oo)`

A

for atleast one x in the interval `[1, oo), f(x + 2) - f(x) lt 2`

B

`underset(x rarr oo)(lim) f'(x) = 1`

C

for all x in the interval `[1, oo), f(x+2) - f(x) gt 2`

D

f'(x) is strictly decreasing in the interval `[1, oo)`

Text Solution

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The correct Answer is:
C
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