Section 4.3

Main Points: Section 4.3 discusses global maximums and global minimums. A global max or min occurs where the function is greater or less than all other points on the function. The function, f, has a global maximum at p if f(p) is greater than or equal to all values of f. It has a global minimum at p if f(p) iis less than or equal to all values of f. To find a global max or min of f on an interval including endpoints, compare values of f at all critical points on the interval and also the endpoints. However, a function defined as domain is all real numbers or on an interval exluding endpoints may or may not have a global max or min. To see if the function has a global max or min in this case, simply find values of f at all the critical points and sketch the graph.

Challenges: I've already done this section, except my teacher called them "absolute" max or min. However, some students may get confused if they forget to include the endpoints when checking for global maxes or mins since this could affect their final answer.

Reflections: I understand that global maxes or mins give the highest or lowest value of the function, but how can you apply that into real life situations? The book gave an example about gas, but other than that, what would you use the second derivative and global maxes/mins for?