Question 988976
We are working with the limit definition of the first derivative, that is
Limit as h --》0 of ( f(x+h) - f(x) ) / h
We are given f(x) = 1 / x
We apply the given function to the limit definition
Limit as h --》0 of ( 1/(x+h) - 1/x ) / h =
( x - x - h ) / (x(x+h)h ) =
-h / (x^2+xh)h =
-1 / x^2
Note that the xh term becomes 0 as h --》0
f(3) = 1 / 3
m = f'(3) = -1 / 3^2 = -1 / 9