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finding intervals differentiation question?

when finding the interval for a increasing or decreasing function do you do f'(x) greater/less than equal to or just greater/less than 0 and why?
(edited 2 months ago)
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Original post by million.
when finding the interval for a increasing or decreasing function do you do f'(x) greater/less than equal to or just greater/less than 0 and why?

As far as I know, at a level the terminology is used for the gradient > 0 and < 0, which is sometimes referred to as strictly increasing and strictly decreasing. Id guess its so they can distinguish it from stationary points where the gradient is zero.
(edited 2 months ago)
By definition of an increasing function, the constant function is increasing (despite English tells you otherwise). So yes we do need equality here.

EDIT: Note the subtle difference between increasing and strictly increasing.
(edited 2 months ago)

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