I am totally lost on difference quotients. Can someone show me how to figure out this problem ....?

Question

difference quotient = f(x+h) - f(x) / h

find the difference quotient for: f(x) = 3x+2

Thank you in advance for any help you have to offer.

Answer 1

f (x + h) = 3 (x + h) + 2
f (x + h) = 3 x + 3 h + 2
f (x) = 3 x + 2
f (x + h) - f (x) = 3 h

[ f(x + h) - f(x) ] / h then becomes:-
3 h / h
3

Answer 2

Use the definition you provided:
difference quotient = (f(x+h) - f(x))/h

Taking this one step at a time,

1) f(x+h) means plug in "x+h" for "x" in f(x). So

f(x+h) = 3(x+h) +2 => 3x+3h+2

2) now subtract f(x) from this result:

3x+3h+2-(3x+2) => 3h

3) Now divide the result by h: 3h/h => 3.

So the answer is 3.

Hope this helps.