Linear Approximation*

  • Linear approximation is an approximation of a general function using a linear function.

  • They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.

  • In essence, linear approximation is using an equation of a tangent line based on a point close to a value to approximate that value of a function rather than plugging it directly into the function.

  • It tends to be easier to plug the input into an equation of a tangent line rather than the function itself.

Essential Questions

How can derivatives be used to approximate values of a function?