11. To every point on this surface, there is an infinite number of tangent lines . 12. Take a small step along that tangent line up to a point A _ 1. 13. Geometrically, the derivative is the slope of the tangent line to the graph of at. 14. The tangent line is the best linear approximation of the function near that input value. 15. For example, a curve that crosses itself doesn't have a unique tangent line at that point. 16. So, the other intersection point between the tangent line and the graph of is the point 17. The angle between two curves intersecting at a point is the angle between their tangent lines . 18. This hypotenuse is parallel to the tangent line of the integral curve at that corresponds to. 19. The slope M should be, most accurately, the slope of the tangent line at x = a. 20. In this case, we use the tangent line to the curve at this point as our line.
