Horizontal Tangent Line

Definition

A horizontal tangent line is a line that is parallel to the x-axis and touches a curve at a specific point without crossing it. It indicates that the slope of the curve at that point is zero.

Related terms

Derivative:

The derivative of a function represents its rate of change at any given point. For a function to have a horizontal tangent line at a specific point, its derivative must be equal to zero at that point.

Slope:

The slope of a curve represents how steep or shallow it is at any given point. To have a horizontal tangent line, the slope of the curve must be zero at that specific point.

Critical Point:

A critical point occurs when either the derivative does not exist or when it equals zero. Having a critical point can indicate the presence of either vertical or horizontal tangent lines.