Explanation:
This statement is generally true and can be proven mathematically. In calculus, the tangent line to a curve at a given point is defined as the line that passes through the point and has the same slope as the curve at that point.
If a tangent line touches a curve at more than one point, it means that it has the same slope as the curve at those points, which would mean that the curve has two or more points with the same slope. However, this is not possible for a continuous curve. If a curve has two or more points with the same slope, it would have a point of inflection, a sharp corner, or a cusp at those points, which would break the continuity of the curve.
Therefore, for a continuous curve, the tangent line can touch the curve at only one point. This property is important in calculus and is used to find the slope of the curve at a specific point and to approximate the behavior of the curve near that point.