Question

When is the tangent line on a curve perpendicular to a line?

A. At the maximum point
B. At the minimum point
C. At the inflection point
D. At the point of intersection

Answer 1

The tangent line on a curve is perpendicular to a line at the point of intersection.

Step-by-step explanation:

The tangent line on a curve is perpendicular to a line when the slope of the curve is the negative reciprocal of the slope of the line. In other words, if the line has a slope of m, then the tangent line on the curve will have a slope of -1/m.

So, when do we have the negative reciprocal of a slope? It happens when the slope of the line is 0. Therefore, the tangent line on a curve is perpendicular to a line at the point of intersection, which is the answer choice D.