Singular point of a curve

Imagine drawing a line on a piece of paper. Now, imagine that line having a point where it looks a bit different from the rest of the line. This point is called a "singular point."

Think of it as a bump or a dip on the line. It's like a little hiccup in the smoothness of the line. In math, we look at curves or lines in a more complicated way than just drawing them on a piece of paper. We use something called "calculus" to study them.

In calculus, we use a fancy word called "derivative" to find out how the line is changing. And when we look at the derivative of a curve and find a point where it drastically changes or stops changing altogether, we call that point a singular point.

It's kind of like if you were driving a car on a straight road, and suddenly there was a big bump or a pothole. The car would have to slow down or change direction to avoid crashing. That's what happens with a curve when it hits a singular point – it has to slow down or change direction because something weird is happening there.

So, a singular point is a special point on a curve or line where something unusual happens, and we can use math to study it!