Midpoint method

Midpoint method is a way to figure out the approximate value of a function at a certain point by using a formula that tells us what the function is doing halfway between two given points.

Imagine you're playing a game with your friend, and you're trying to guess where a ball will land after it's thrown. You know the starting point and the speed of the ball, but you're not sure exactly where it will end up. One way to make a good guess is to watch the ball closely at two different times and see how far it travels in between.

The midpoint method works in a similar way. To use it, we pick two points on the graph of the function we're interested in, and figure out what the function is doing halfway between those points. We do this by finding the average of the function values at those two points. This gives us an approximate value of the function at the midpoint.

Then we can repeat this process, using the midpoint we just found and one of the original points to find another midpoint. This gives us an even better guess for the value of the function at the midpoint.

We can keep doing this over and over, using increasingly smaller intervals between points, until we get a very accurate estimate of the function value at the point we're interested in. It's like zooming in on the graph and getting a closer and closer look.

Overall, the midpoint method is a simple but effective way to estimate the value of a function at a certain point, by using the concept of averages and breaking down the problem into smaller intervals.