On-line Math 21

2.4  Applications of the derivative.

Example 1 Find an approximate value of

___ Ö4.2   .

Solution:

f(x) = Öx in this example (you have to figure out the function in these examples). Then, a = 4 , Dx = 0.2 , and we have:

f(a+Dx) = f(a)+f¢(a)Dx   ___ Ö4.2   = Ö4+ 1 2Ö4 0.2 = 2+ 1 4 0.2 = 2.05.

By the way, my computer said

___ Ö4.2   = 2.04939015319192.

Of course, the computer also gives an approximation. We usually assume that the computer approximation is closer to the real answer than some by-hand linear approximation. But it isn't, necessarily. The computer uses a fancy approximation scheme for any of the functions it is programmed to compute. Many of those approximations are based on things like linear approximation. So, the computer approximation has the same sources of error as these methods. In addition, the computer does not indicate how accurate the approximation is that it is using. Often the digits displayed are not all accurate.

Copyright (c) 2000 by David L. Johnson.