How to Find Horizontal Tangent Lines?

Horizontal lines can be defined as line segments on a coordinate plane in which y – coordinate remain same and x – coordinate change according to the values. It is a line which is moving either on left or right side. It is a Straight Line on a plane which lies along y – axis, all points on these lines are same. Slope of horizontal line is always zero. They are mainly moving with horizontal axis. Here we will discuss how to find horizontal Tangent lines.

To check reverse value of a function we will use horizontal lines test. It is also useful for finding the tangent of a line in geometric mathematics. Horizontal lines are always parallel to x - axis in case of plane. Equation of horizontal line is given as:
y = q, here 'q' is the line on y- axis.

Tangent lines and their equations can be solved with help of first and second Derivatives. Now we will solve tangent line problem and also see their solutions with help of first derivatives. Let's take an example:
Problem: We have a equation y = x² – 2x, then find all points of a graph where tangent line is parallel to x- axis?
Solutions:
(1) All lines which are parallel to x- axis and have Slope value equals to zero.

(2) Now find out first derivative of given equation.
                        Y1 = 2x – 2

(3) Then put values of 'x' in the equation, on putting value y1 = 0 we get;
                        2x - 2 =0

(4) Now solve above equations to find the value of 'x',
                 2x - 2 = 0,
                       2X = 2,
                       X =1,
(5) Coordinates of equations y = x2 - 2, for x = 1 and y = 0.

(6) Coordinates of tangent lines which are parallel to x - axis are (1, 0).