Tangent lines are straight lines that touch (but do not cross) curves at one specific point. They represent the instantaneous rate of change or slope of the curve at that particular location.
Slope measures how steep or slanted a line or curve is. In the context of tangent lines, slope represents the rate of change and helps determine how fast the curve is changing at a particular point.
The derivative of a function provides the slope of its tangent line at any given point. It allows us to find the equation of the tangent line and understand local behavior more precisely.
Instantaneous rate of change refers to how fast a quantity is changing at an exact moment in time, as indicated by the slope of the tangent line. It helps analyze motion or growth patterns in various real-world scenarios.