watch :

https://youtu.be/qb40J4N1fa4

question:

Around 8:40 he says that you choose a point in any direction to find the derivative, like 0.01 away, but at 10:10 he says a condition is to choose a value on the circle to find the tangent line and keep the expression equal to zero. So is finding the tangent essentially the same as choosing a point that's very close?