Minimize the product of two real numbers while their difference is constrained.

Minimize the size of a piece of paper while an area on the paper and the margins around the area are constrained.

Minimize the cost of a rectangular fence while its area is constrained.

?When you're looking for extrema in a closed interval, you're looking for the highest and lowest points that the function attains in the interval, including at the endpoints of the interval. For that reason, the candidates for extrema will always be only any critical points that lie inside the interval and the endpoints of the interval.

Once we have all the information about the critical and inflection points of a function, where it's increasing and decreasing and concave up and concave down, and where its asymptotes exist, we can sketch the graph of the function.

Find the slant asymptote of a function by using polynomial long division to simplify the function.

In this video, you'll learn how to find the horizontal asymptote of a rational function.

The vertical asymptotes of a function exist wherever the function is undefined.

The second derivative test lets you say where a function is increasing and decreasing, and therefore where it has local extrema. Just find the function's critical points, then find the second derivative of the function and evaluate each of the critical points in the second derivative.

Use the first derivative test to say where the function is increasing and where it's decreasing. You just need to find the function's critical points, and then plug a value in between each critical point into the function's first derivative to test each interval.