Monotonicity of Functions

Pure Mathematics — Second Secondary

Common mistakes

Key points

Judging monotonicity from one pointknowing the value at one point is not enough to decide whether a function increases or decreases.

Leaving out the intervalnever write “the function is increasing” without stating where.

Confusing monotonicity with signa positive function is not necessarily increasing, and a negative function is not necessarily decreasing.

Losing track of the inequality directionwhen a < b, the difference b − a is positive, and this is the key to analysing f(b) − f(a).

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