Linearization and Tangent Line Approximation
The line tangent to a function (that's differentiable) at is also called the linearization of at .You can use the linearization of a function at to approximate values of near . This technique is also called tangent line approximation. Here's an example. Suppose someone asks you to estimate (without a calculator).
Without using any calculus, you know is a number between which two consecutive integers? Why?
How does what you observed in the applet related to Good Definition #2 of a tangent?
Use the linearization of at to approximate .
Use tangent line approximation to estimate the cube root of . (This means you'll have to determine what function and linearization to use.)