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Continuity and Differentiability|Increasing and Decreasing functions#!#Strictly Increasing a d Decreasing functions

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A function f is said to be increasing/strictly increasing/decreasing/strictly decreasing at x_0, if there exists an interval I containing x_0, such that f is increasing /strictly increasing /decreasing /strictly decreasing, respectively, in I. Which of the following statements regarding the above definition is FALSE?