Question

Find and simplify the difference quotient
f(x + h) − f(x)/h for the following function. f(x) = 3x2 + 3x − 3

Answer 1

i got 6x+3h+1 but apparently thats wrong..

Answer 2

What is \(f(x+h)\)?

Answer 3

Let's do it one piece at a time.

Answer 4

3(x+h)^2+3

Answer 5

\[
3(x+h)^2+3(x+h)-3
\]

Answer 6

Expand and simplify that for me.

Answer 7

3x^2+6xh+3h^2+3x+3h-3-3x^2-3x+3= 6xh+3h^2+3h/ h

Answer 8

i just now noticed that for 3(x+h) i forgot to put 3 on both sides and thats why i got the wrong answer! it should be 6x+3h+3 as the answer

Answer 9

That looks about right, now what happens as \(h\to 0\)?