Difference quotient

The difference quotient is like a game we play with numbers. Imagine you have a big ball and you want to know how fast it is rolling downhill. But you can't see the ball, so you have to use math to figure it out. First, you measure the distance the ball travels in a specific time, let's say one second. Then, you measure the distance the ball travels in the next second. You subtract the first distance from the second distance, and that gives you the difference between how far the ball rolled in one second and how far it rolled in the next second. Finally, you divide that difference by the time it took to roll, which is one second. That is the difference quotient. It tells you how fast the ball was rolling downhill in that specific moment. So, whenever you want to know how fast something is moving, you can use the difference quotient formula.