How to Find Equations of Tangent Lines

Table of contents:

How to find the equation of a tangent line?

Unlike a line, the slope of a curve constantly changes as you move along its graph. Mathematics introduces students to the idea that each point on this graph can be described as an instantaneous slope or rate of change. The tangent line is a line with this slope, passing through this exact point on the graph. To find the equation of a tangent line, you need to find the derivative of the original equation.

Represent the function and the tangent line

A graph will allow you to easily understand the problem and check if your answer makes sense. Represent the function on graphing paper using a graphing calculator as a reference, if necessary. Represent the tangent line by passing it through the given point (remember that the tangent line passes through this point and has the same slope as the graph at this point).

Find the first derivative to determine the equation for the slope of the tangent line

For the function f (x), the first derivative f '(x) represents the equation of the slope of the line tangent to any point of f (x). There are several ways to calculate the derivative.

Enter the value of x for the point you have chosen

ARead the problem to determine the coordinates of the point for which you are looking for the tangent line. Enter the x coordinate of this point in f '(x). The result is the slope of the tangent line at this point.