# How do you find the equation of tangent to a curve?

Table of Contents

## How do you find the equation of tangent to a curve?

To determine the equation of a tangent to a curve: Find the derivative using the rules of differentiation. Substitute the (x)-coordinate of the given point into the derivative to calculate the gradient of the tangent.

### How do you substitute a tangent for a straight line equation?

Substitute \\ (x = – ext {1}\\) into the equation for \\ (g’ (x)\\): Substitute the gradient of the tangent and the coordinates of the point into the gradient-point form of the straight line equation.

#### How do you calculate the gradient of the normal and tangent?

Use the gradient of the tangent to calculate the gradient of the normal: Substitute the gradient of the normal and the coordinates of the given point into the gradient-point form of the straight line equation. Determine the equation of the tangent to the curve defined by \\ (F (x)=x^ {3}+2x^ {2}-7x+1\\) at \\ (x=2\\).

**What is the gradient of a curve at a given point?**

At a given point on a curve, the gradient of the curve is equal to the gradient of the tangent to the curve. The derivative (or gradient function) describes the gradient of a curve at any point on the curve. Similarly, it also describes the gradient of a tangent to a curve at any point on the curve.

**How to find the gradient of the tangent of a point?**

Use the rules of differentiation: To determine the gradient of the tangent at the point \\ (\\left (1;3ight)\\), we substitute the \\ (x\\)-value into the equation for the derivative. Substitute the gradient of the tangent and the coordinates of the given point into the gradient-point form of the straight line equation.

## What is the slope of tangent to circle at D=(4,-2)?

The tangent to circle at D= (4,-2) is perpendicular to radius CD. Slope of CD is 4/-3 so slope of tangent is 3/4.