Local linearization

The  exercise appears under the Differential calculus Math Mission. This exercise uses local linearization and the equation of a tangent line to approximate functions.

Types of Problems
There are three types of problems in this exercise:


 * 1) Use the approximation to find the function and the point: This problem provides an expression that provides an approximation to the value of a function. The student is asked to use the expression to determine the function and the point.Loclin1.png
 * 2) Find the linear approximation: This problem provides a function and a point. The student is asked to find the linear approximation and select it from a multiple choice list.Loclin2.png
 * 3) Apply the linear approximation: This problem provides a function and a value for which the value is being sought. The student is asked to find the linear approximation and then apply it to find the appropriate approximation.Loclin3.png

Strategies
Knowledge of derivatives and the process for linear approximation are encouraged to ensure success on this exercise.
 * 1) For a function f(x) at the point x=a, the linear approximation is given by L(x)=f(a)+f'(a)(x-a).
 * 2) Approximations are necessary, exact values will not be accepted.

Real-life Applications

 * 1) Most of the problems in this subsection are applications in some sense, so the majority of the exercises are applications also.
 * 2) Local linearization is also applied with differentials as an application of derivatives.