Subtangent
A subtangent is like finding the slope of a line, but for a curve. Imagine you have a curve like a smiley face or a bouncing ball. The subtangent is the slope of a line that just touches the curve at one point, like when you put your finger on the curve and move it along until it is sliding next to the curve at one spot.
Now, imagine you have a piece of string that is really long and flexible, like spaghetti. You can lay the string on the curve so that it is just touching at one point. Then you can straighten out the string so it is flat, and lay a ruler on the string to measure how steep the slope is at that one spot. That slope measurement is the subtangent! It tells you how quickly the curve is going up or down at that one point.
Sometimes we use subtangents in math to help us figure out other things about the curve, like how fast it is changing or what its shape is like. But at its heart, a subtangent is just a way to describe how much a curve is tilting or sloping at one specific point.
Now, imagine you have a piece of string that is really long and flexible, like spaghetti. You can lay the string on the curve so that it is just touching at one point. Then you can straighten out the string so it is flat, and lay a ruler on the string to measure how steep the slope is at that one spot. That slope measurement is the subtangent! It tells you how quickly the curve is going up or down at that one point.
Sometimes we use subtangents in math to help us figure out other things about the curve, like how fast it is changing or what its shape is like. But at its heart, a subtangent is just a way to describe how much a curve is tilting or sloping at one specific point.