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.