A tangency point of a curve and a straight line occurs
A)whenever their slopes are equal at the same x value
B)when they touch at a point but don't cross
C)when the lines cross
D)when they are perpendicular to each other

Question

Quizplus · Accepted Answer

A tangency point occurs when the curve and the straight line touch at a single point but do not cross each other. This means that they have the same slope at that point, but it is possible for them to have different slopes at other points. If the slopes were always equal at the same x value, then the curve and the straight line would coincide and not touch at a single point. If the lines crossed, they would not have a tangency point but an intersection point. If they were perpendicular to each other, they would have infinitely many points of contact, not just one tangency point.

A Tangency Point of a Curve and a Straight Line