Maxima and minima

Imagine you have a playground with a very tall slide and a very low swing. You want to find out the highest point you can reach on the slide and the lowest point you can reach on the swing.

The highest point on the slide is called the "maximum" and the lowest point on the swing is called the "minimum."

In math, we use these words to talk about the biggest and smallest values of a function. A function is like a machine that takes in a number and spits out another number.

So, if we graph a function on a coordinate plane, the maximum is the highest point on the graph, and the minimum is the lowest point on the graph.

To find the maximum and minimum, we need to look for the highest and lowest points on the graph by checking every point on it. This process is called "optimization."

Just like on the playground, finding the maximum and minimum can help us make better decisions in real life. For example, if we have a business and we want to increase profits, we can use optimization to find the best prices for our products that will give us the most money.