Question

Which of the following coordinate points lie on the curve where x = 1 and the tangent to the curve is horizontal, or is it stated that no points exist?

A) (1, 1)
B) (1, 2)
C) (1, 3)
D) No points exist

Answer 1

Without additional information about the function or its derivative, we can't determine which point has a horizontal tangent. However, since all points fulfill the condition x = 1, they lie on the curve defined by x = 1, but we need more data to find the point with the horizontal tangent.

Step-by-step explanation:

The student asked which of the following coordinate points lie on the curve where x = 1 and the tangent to the curve is horizontal. A horizontal tangent implies that the slope of the tangent (and therefore the slope of the curve at that point) is zero.

All the given points, (1, 1), (1, 2), and (1, 3) have x-coordinate equal to 1; however, without additional information about the function or its derivative, we cannot determine which, if any, of these points has a horizontal tangent. But as all points fulfill the condition of x being 1, we can deduce that the points lie on the curve defined by x = 1. The statement that 'no points exist' can be disregarded since x = 1 adequately describes a line and there can be points on it with a horizontal tangent if it is part of the curve. The actual curve's equation or further information is necessary to identify exactly which point(s) have a horizontal tangent.