# How do you calculate the tangent of a curve?

## How do you calculate the tangent of a curve?

In order to find the equation of a tangent, we:

- Differentiate the equation of the curve.
- Substitute the value into the differentiated equation to find the gradient.
- Substitute the value into the original equation of the curve to find the y-coordinate.
- Substitute your point on the line and the gradient into.

**How do you find the tangent between two curves?**

The slope of the tangent line will be given by inserting a point x=a into the derivative. Hence, it makes sense to start by finding the derivative of each function. Let f(x)=x3−3x+4 and g(x)=3×2−3x . So, the functions will share tangent lines at the points x=0 and x=2 .

### How do you find the point of tangency between two functions?

Find the derivative. For the tangent lines, set the slope from the general point (x, x3) to (1, –4) equal to the derivative and solve. Plug this solution into the original function to find the point of tangency.

**What does it mean for two curves to be tangent?**

The angle between two curves at a point where they intersect is defined as the angle between their tangent lines at that point. More specifically, two curves are said to be tangent at a point if they have the same tangent at a point, and orthogonal if their tangent lines are orthogonal.

#### How do you find the equation of the tangent line to the curve at a given point?

To determine the equation of a tangent to a curve: Substitute the x-coordinate of the given point into the derivative to calculate the gradient of the tangent. Substitute the gradient of the tangent and the coordinates of the given point into an appropriate form of the straight line equation.

**What is tangent to curve?**

tangent, in geometry, the tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point. It may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve as the second point approaches the first.

## How do we find point of tangency?

A tangent is an object that just barely bumps up against a circle or a curve and touches at one point. The point where the tangent touches the curve is the point of tangency. Lines or segments can create a point of tangency with a circle or a curve.

**Can 2 curves be tangent to each other?**

We say that two curves are tangent to each other at a point P, if both these curves pass through P and have the same tangent line at P.