Answer to Question #14679 in Real Analysis for Paulo
Then the derivative:
f'(x) = 1 + 4x * sin (1/x) - 2cos (1/x) when x is not equal to 0 and
f'(0) = 1.
For any neighbourhood of x=0 the derivative f'(x) has positive and negative values.
So, there is no neighbourhood of x=0 such that f(x) is monotone there.
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