Question
Given the function (f(x+h)-f(x))/h simplify your answer as much as possible. f(x)=3x^2-1
Answers
Anonymous
f(x+h) = 3 (x^2 + 2 h x + h^2) - 1
= 3 x^2 + 6 x h + 3 h^2 - 1
f(x) = 3 x^2 - 1
---------------------- subtract
(f(x+h)-f(x)) = 6 x h + 3 h^2
divide by h
(f(x+h)-f(x))/h = 6x + 3 h
that is it but note that as h ---> 0
that is 6 x, which is the derivative of the function
= 3 x^2 + 6 x h + 3 h^2 - 1
f(x) = 3 x^2 - 1
---------------------- subtract
(f(x+h)-f(x)) = 6 x h + 3 h^2
divide by h
(f(x+h)-f(x))/h = 6x + 3 h
that is it but note that as h ---> 0
that is 6 x, which is the derivative of the function