I'm trying to find all slope zero tangent lines of the original equation
A horizontal tangent line is a line that is parallel to the x-axis and touches the graph of an equation at only one point. This point is called a point of tangency, and the slope of the tangent line at this point is equal to 0.
To find the horizontal tangent line of an equation, you need to take the derivative of the equation and set it equal to 0. The x-value of the resulting solution will be the x-coordinate of the point of tangency. Then, substitute this x-value back into the original equation to find the y-coordinate of the point of tangency. Finally, use the point-slope formula to write the equation of the horizontal tangent line.
Yes, an equation can have more than one horizontal tangent line. This typically occurs when the graph of the equation has multiple horizontal sections or curves.
A horizontal tangent line represents a point where the slope of the original equation is equal to 0. This can also be interpreted as a point where the rate of change of the equation is 0, or where the function is at a maximum or minimum value.
Yes, there are a few special cases when finding horizontal tangent lines. One case is when the original equation is a constant function, in which case the entire graph is a horizontal tangent line. Another case is when the derivative of the equation is undefined, in which case there is no horizontal tangent line. Finally, if the derivative of the equation is always equal to 0, then every point on the graph can be considered a point of tangency and the equation will have an infinite number of horizontal tangent lines.