# Normal lines and Tangent lines

## Thesis

How to understand all concepts of Normal line and Tangent line and how to solve any problem.

## Definition of Normal line and Tangent lines

Tangent line-A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.

Normal line-is the curve at a point which is the line perpendicular to the tangent at that point.The slope of a line perpendicular to the tangent line is opposite,reciprocal of the tangent line.

## Another part to tangent lines is horizontal tangent line and here is how you solve them.

1. Find f'(x) and set that derivative=0 (slope of hora. line is 0)

2. Solve for x.

3.Substitue that value of x into the original function to find the y-value of the point of tangency.

## How to solve a Tangent line problem

1.You may have to find the y -value of the point on the graph by substituting in the given x-value into the original equation. 2.Find the derivative of f.3.evaluate f'(x) to get the slope of the graph must be a number.4.Substitute the given point and the slope of the derivative at that value into the point-slope formula.

## How to solve a Normal line problem

1.You may have to find the y -value of the point on the graph by substituting in the given x-value into the original equation. 2.Find the derivative of f.3.Evaluate f'(x) to get the slope of the graph must be a number.4.Then find the reciprocal of that number and thats your new slope.5.Substitute the given point and the slope of the derivative at that value into the point-slope formula.