1. ## Using linear approximation

Suppose you have a function f(x) and all you know is that f(3) = 25 and the graph of its derivative is:

http://img86.imageshack.us/img86/5896/sd...

Use linear approximation to estimate f(3.1):

any ideas?

2. The derivative gives the rate of change of a function. From the graph, f'(3) = 3. This is a change of three units over one unit along the x-axis. you are going 3.1 - 3 = .1 units so you will have a change of .1[f'(3)].

3. also note that,
$\displaystyle f(x)$ is approximated by $\displaystyle f(x_0) + f ' (x_0) dx$ where$\displaystyle x_0 = x - dx$
then use the data given by the previous post.. Ü