calculus 1 problem locate the extrema of fx x on the interv

Solution

f(x) = [[x]] is called the greatest integer function which is a function in which for every x, the function is rounded down to the nearest integer.

The formal definition: the Greatest Integer Function, [[x]], is a function in which the output is the largest integer that is less than or equal to x

Examples:
f(3) = 3
f(0) = 0
f(3.1) = 3
f(3.9) = 3
f(3.99999) = 3
f(-0.5) = -1
f(-2) = -2

In essence, for every integer value, f(x) = x.
In essence, for every non-integer value, f(x) is rounded down to the nearest integer

Graphically, f(x) = [[x]], looks like what we call the step function (I tried drawing, but Cramster\'s Custom Diagram feature always seems to fail). However, it is basically a piece-wise function made of horizontal line segments.

Therefore the absolute max would occur at x = 2

Therefore the absolute min would occur at x = -2

BOL