ElPrepha-Cotas Superiores -Inferiores-Introducciòn

Understanding Upper and Lower Bounds of Functions

Introduction to Upper Bound

• The speaker introduces the concept of upper bounds in functions, emphasizing the need to understand when a function is bounded above.

• An upper bound exists if there is a real number n such that for any value taken from the function, it remains less than or equal to n .

• The maximum height of a curve within an interval represents its upper bound; this relates directly to the function's maximum and minimum values.

Calculating Upper Bound

• To find the upper bound of a function over an interval, one must determine the maximum height reached by that function.

• For example, if evaluating a point A , one might find that its maximum height is 1.8 within a specified interval.

• Any value below this maximum (e.g., 1, 2, 3...) will be considered lesser than or equal to this upper bound.

Transitioning to Lower Bound

• The discussion shifts towards lower bounds, which are defined as values where any output from the function will always be greater than or equal to this lower limit.

• The speaker explains that finding a lower bound involves identifying the minimum absolute value achieved by the function over an interval.

Example of Lower Bound Calculation