Derivatives by the four step quotient process

Question

These are the questions:

(i) For the function, f(x)=3x^2 - x, find the derivative by the four-step difference quotient process.

(ii) Now calculate the derivative using differentiation rules, and in a complete sentence, explain whether or not your answer agrees with your calculation from (i).

For part (i) I got 6x+3h-1, and for part (ii) I used the power rule to get 6x-1, but I am not sure whether these answers agree. For the first question, since I followed the four step process, I also calculated the limit as h approaches zero which ended up giving 6x-1, but I'm not sure if that means anything, can someone explain whether these calculation agree with each other.

Answer 1

In step 4 of the 4-step process, as you mentioned, you calculate the limit as h approaches zero. This is indeed part of the process and makes the answer turn out to be 6x - 1. So the result of (i) is NOT "6x+3h-1" but instead "6x -1" therefore your answers agree.