)Loppyfoot said:
Points of tangent line are the points on a curve where the slope of the tangent line is equal to the slope of the curve at that point. In other words, they are points where the curve and the tangent line touch and have the same direction.
Vectors can be used to represent the slope of the curve and the slope of the tangent line at a given point. By finding the intersection of these two vectors, we can determine the point of tangent line on the curve.
The process involves finding the derivative of the curve at a given point, which represents the slope of the curve. Then, using the same point as a starting point, another vector is created to represent the slope of the tangent line. The point of tangent line is then found by finding the intersection of these two vectors.
One limitation is that the curve must be differentiable at the given point in order for the derivative to exist. Additionally, the accuracy of the result depends on the precision of the vectors used.
Yes, this method can be applied to any differentiable curve, as long as the necessary vectors can be created to represent the slope of the curve and the slope of the tangent line at a given point.