# 3633: Algebra and Functions - Functions - Strictly increasing/decreasing

This display shows the difference between increasing/decreasing and strictly increasing/decreasing functions.

The gradient of $f(x) = {x^3} + 1$ is 0 at $x = 0$, but it is still strictly increasing at this point, because to the left $f(x)$ is less, and to the right $f(x)$ is more ($\forall a,b:a < b \Rightarrow f(a) < f(b)$).

The gradient of $f(x) = - {x^3} + 1$ is 0 at $x = 0$, but it is still strictly decreasing at this point, because to the left $f(x)$ is more, and to the right $f(x)$ is less ($\forall a,b:a < b \Rightarrow f(a) > f(b)$).
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