Discuss some techniques for solving discrete optimization problems (e.g., integer programming, branch and bound).

Aug 29, 2014 ... The extreme value theorem says that for a continuous function on a closed interval there will be a minimum and maximum value. Jun 26, 2013 ... You can find the extrema of a function by drawing a parabola between 3 points, finding the vertex, then repeating. Whereas the boundedness theorem states that a continuous function defined on a closed interval must be bounded on that interval, the extreme value theorem goes ... Feb 12, 2012 ... So, finding extreme values, you must assume that y = f ( x ) \displaystyle y=f(x) y=f(x) or x = f ( y ) \displaystyle x=f(y) x=f(y) because if f ... The Extreme Value Theorem guarantees both a maximum and minimum value for a function under certain conditions. Jul 9, 2021 ... All local maximums and minimums on a function's graph — called local extrema — occur at critical points of the function (where the ... Extreme value theorem. If f is a continuous function on a closed interval I = [a, b], then f has both a maximum value and a minimum. For example, “sin(x) sin ⁡ ( x ) has a maximum at π/2, π / 2 , and the maximum of sin(x) sin ⁡ ( x ) is 1. 1 . ” Consider Figure 3.1.3. The function displayed ... ... extreme values of a function; we must test each critical point separately to determine if it does indeed yield a local maximum or minimum. There are some ... Apr 27, 2019 ... In this section, we look at how to use derivatives to find the largest and smallest values for a function.