1. ## the derivative

Find approximate values for f '(x) at each of the x-values given in the following table. (Note: For x = 0, 5, 10, and 15 use the interval to the right. For x = 20 use the interval to the left.)

X = 0 5 10 15 20
f(x) = 110 80 50 43 35
f`(x) = ? ? ? ? ?

ok this is the problem that it gives me, and im not sure where to go...any help would be much appreciated

2. Originally Posted by mer1988
Note: For x = 0, 5, 10, and 15 use the interval to the right. For x = 20 use the interval to the left.
Always use your note. Always. If there is some other way to proceed, do that second.

f'(x) -- What is it? Do you have the definition that relates it to "slope"? that is what you need on this one.

Slope = (Change in y)/(Change in x) = (Change in f(x))/(Change in x)

Using the sugested approximation

f'(x) for x = 0 is approximately (f(5) - f(0))/(5 - 0) = (80-110)/(5-0) = -30/5 = -6

Note: It doesn't much mater which way you subtract them, as long as you are consistent.

(110-80)/(0-5) = 30/(-5) = -6 -- Still good.
(110-80)/(5-0) = 30/5 = +6 -- NO good.