Question

f(x)=7x+2

compute and simplify the difference quotient
f(a+h)-f(a)/h

Answer 1

I kind of understand this concept, I just can't wrap my head around it.

Answer 2

\[\frac{7a+7h+2-7a-2}{h}=7\]

Answer 3

I can get that f(a+h) is 7(a+h), but I can't see how to make the other into +2-[7a+2]

Answer 4

the other is 7a+2 simply

Answer 5

I just don't get when the a and h mean I guess, so I can't see how to relate them to the 7x+2

Answer 6

it's like trying to understand parallel dimensions or something lol

Answer 7

If it's f(cat), you just replace x by cat in the equation. Take whatever in the parenthesis and replace x with it

Answer 8

hmmm, maybe I'm thinking about it backwards

Answer 9

why isn't it 7(a+h)+2-7...oh wait thats whats throwing me, the -f

Answer 10

so that part should be written as -(7a+2) but i don't see why the 7 is in the parenthesis this time

Answer 11

Just simplify the whole thing, write what you got here.

Answer 12

7a+7h+2-7a-2

Answer 13

over h

Answer 14

Then you have it.

Answer 15

Do you get it now?

Answer 16

yea, kinda. I think if I just keep writing it over and over I'll just know what to do and be ok

Answer 17

This shouldn't be hard, all you do is replace 'x' in the equation by the stuff in the parenthesis.

Answer 18

yea, I know, thats whats really frustrating about it haha. what about when the equation is x^2+10x-14?

Answer 19

I got (a+h)^2-10(a)-14

Answer 20

Same stuff. Replace x

Answer 21

No. f(a+h) and f(a) are two separate equations. You gotta replace separately.

Answer 22

oh ok, well, would that be right for the first half?

Answer 23

no

Answer 24

how about (a+h)^2+10(a+h)-14 -(x)^2+10(a)-14

Answer 25

Don't forget your parenthesis :)

Answer 26

oh, and it would be -(a^2+10(a)-14) not x

Answer 27

got it! thanks @absolutemaster, you are the master

Answer 28

absolutely

Answer 29

haha no prob ;)