The First Derivative Test is a useful tool for finding local high and low points (maximums and minimums) of a function. Here’s how it works, in simple steps:

1. Find Critical Points: First, you look for critical points. These are places where the derivative, which we write as $f'(x)$, is either zero or doesn’t exist. These points are key to understanding the function!

2. Analyze Intervals: Then, pick test points in the ranges (or intervals) between your critical points. You will check what sign $f'(x)$ has at these test points.

3. Determine Behavior:

   • If $f'(x)$ goes from positive to negative at a critical point, you have a local maximum (a high point).
   • If $f'(x)$ goes from negative to positive, that’s a local minimum (a low point).

It’s like being a detective! You gather clues to figure out where the high and low points are on a graph.

Using this method really clears things up and makes solving optimization problems much easier!