1 ACEs are commonâ¦nearly two-thirds (64%) of adults have at least one. 2  They cause adult onset of chronic disease, such as cancer and heart disease, as well as mental illness, violence and being a victim of violence.  ACEs donât occur aloneâ¦.if you have one, thereâs an 87% chance that you have two or more.
A horizontal tangent line is a mathematical feature on a graph, located where a function's derivative is zero. This is because, by definition, the derivative gives the slope of the tangent line. Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal. To find horizontal tangent lines, use the derivative of the function to locate the zeros and plug them back into the original equation. Horizontal tangent lines are important in calculus because they indicate local maximum or minimum points in the original function.
Both the graph of y = f(x) and the tangent line pass through the point, and the tangent line has the same gradient, 'm', as the function at that point. The normal line to function y = f(x) at the point (x1,y1) is the straight line that passes through the point making a 90 angle with the graph.The gradient of the normal line is -1/m, where 'm' is the gradient of the tangent line at the same point.'m' is the gradient at (x1,y1)). The equation of the normal line to y = f(x) at (x 1 ,y 1) is: The derivative of y = f(x) at (x 1 ,y 1) gives us the gradient 'm'. For example: Calculate the tangent and normal lines to the function: y = x 2, when x = 1. Solution: Part 1, tangent line.