Further Examples: Interval
You can use Max and Min to find the endpoints of intervals.
You can take the union and intersection of two or more intervals.
Using IntervalMemberQ, you can check if an interval is contained in another.
You can also check if a point belongs to an interval.
You can do interval arithmetic with many functions. For example, this command reflects the fact that the square of any real number between -2 and 5 lies between 0 and 25.
Taking the reciprocal gives two distinct intervals.
You can use intervals in many kinds of functions.
Some functions automatically generate intervals.
With ordinary machine-precision arithmetic, this gives an incorrect result.
The interval generated here, however, correctly includes the point 0.
Interval arithmetic is useful in obtaining or proving bounds. Here we define a function ff, which depends on a parameter .
This shows that ff is monotonically nonincreasing in x for all non-negative values of the parameter.