Concave function

Imagine you are playing with a ball and rolling it down a hill. If the hill is steep at the beginning, the ball will roll faster and faster. However, as the hill starts to flatten out towards the bottom, the ball will slow down until it stops completely.

A concave function works similarly to this hill. It starts off steep and then flattens out. In math terms, we can say that a concave function has a decreasing rate of change as the input (x-axis) increases.

Let's say we have a function that represents the height of a rollercoaster track. At the beginning of the track, the coaster climbs up a steep hill. As it reaches the top of the hill, it starts to slow down until it gets to the crest. Then, it speeds up again as it goes down the other side.

This rollercoaster function is an example of a concave function because it starts off steep, flattens out at the top, and then becomes steep again.

In summary, a concave function is like a hill that starts off steep and then flattens out. It has a decreasing rate of change as the input increases.