Derivative test

The derivative test is like a special tool that helps us figure out if a point on a graph is the highest, the lowest, or just a regular point in between.

Imagine you're climbing a mountain and you want to know if you've reached the highest point. The derivative test is like your hiking map and compass that tell you which direction to go.

First, we need to know what a derivative is. A derivative is like a slope on a graph. It tells us how much the graph is going up or down at each point.

Next, we use the derivative to find something called the critical points. These are the points where the slope is zero, which are like the very top, bottom or flat parts of the graph.

Finally, we use the second derivative to determine whether the critical point is a maximum or a minimum or something else. The second derivative is like the steepness of the slope at the critical point. We can see if the slope is curving down or curving up to find out if it's a high point or a low point.

So, in summary, the derivative test is a way to use math to figure out if a point on a graph is the highest, lowest or just a regular point by using the slope and the curvature of the graph.