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A function of real numbers is also called a step function if it is piecewise constant function involving a finite number of inputs. There are two types of step functions. Greatest Integer function (floor function) - A function f(x) is said to be a floor function which possesses biggest integer that is less than or equal to the input value x Smallest Integer function (ceiling function) - A function f(x) is said to be a ceiling function which is composed of the lowest integer that is either bigger or equal to the input value x A step function is also known as staircase function, since it looks like a staircase.
Local minima and maxima (First Derivative Test). A function $f$ has a local maximum or relative maximum at a point $x_o$ if the values $f(x)$ of $f$ for $x$ ânearâ $x_o$ are all less than $f(x_o)$. Thus, the graph of $f$ near $x_o$ has a peak at $x_o$.