The equation of a tangent line is a mathematical representation of a line that touches a curve at one point and has the same slope as the curve at that point.
The equation of a tangent line can be calculated using the derivative of the function at the point of tangency. The derivative gives the slope of the curve at that point, which can then be used with the point of tangency to find the equation of the tangent line.
The equation of a tangent line helps us understand the behavior of a curve at a specific point. It can also be used to find the instantaneous rate of change or slope of a function at a given point.
Yes, the equation of a tangent line can be used to find the equation of the normal line, which is perpendicular to the tangent line. It can also be used to find the concavity of a curve at a given point.
The equation of a tangent line is only applicable at one specific point on a curve and may not accurately represent the overall behavior of the curve. It also assumes that the curve is differentiable at that point.