Part 3/7:
One major reason for utilizing linear approximation is the complexity of calculating ( f(x) ) directly. In many cases, the derivative provides a way to simplify these calculations by using the slope of the tangent line to make educated estimates about nearby points. However, the accuracy of these estimates tends to decrease as we move further away from the point of tangency ( a ).
Example 1: Predicting Turkey Temperature
Let's look at a practical application of linear approximation through an example involving the temperature of a turkey.