Question

given f(x) = x^2 -x+1, find f(2+Δx)-f(2) / (Δx)

Answer 1

i just need some help getting started on this one

Answer 2

You need to replace in the variable x, with everything the f() says. So in your case, you would go like\[\frac{((2+ \Delta x)^2-(2+ \Delta x)+1)-(2^2-2+1)}{\Delta x}\]Now you start simplifying as much as you can :)

Answer 3

ah ok. thanks!

Answer 4

you're welcome, let me know if you need more help on this one.

Answer 5

uh, i'm having a little trouble. i'm not sure if you noticed but i miswrote the original equation.

Answer 6

Can you please provide the corrected equation then?

Answer 7

it's in the open question area now

Answer 8

Yes, I've used that equation that is currently on display to form the expression found in my answer. Do you need help simplifying it?

Answer 9

hmmm, let me take another try at it. i'll post my results.

Answer 10

alright then, remember that the first expression\[(2+ \Delta x)^2 \]is a polynomial of second degree so you need to expand that first.

Answer 11

yes for that i got

Answer 12

4+4(Δx)+(Δx)^2

Answer 13

Yes, you're right. Now the second expression has a (-) sign infront so you need to make sure you factor that in,\[-(2+ \Delta x)\]What did you get for that?

Answer 14

2+3(Δx)+(Δx)^2

Answer 15

You mean the entire nominator looks like that? Like this?\[\frac{2+3 \Delta x + \Delta x^2}{\Delta x}\]

Answer 16

oh i was just doing that one part

Answer 17

You mean\[-(2+ \Delta x)=2 + 3 \Delta x+ \Delta x^2\]

Answer 18

i tried doing it over and got confused. somewhere. i'm going to post what i have.

Answer 19

ok let me see

Answer 20

(4+4(Δx)+(Δx)^2)-2+Δx)+1)-(2^2-2+1) / Δx

Answer 21

that's step 1

Answer 22

correction

Answer 23

(4+4(Δx)+(Δx)^2)-(2+Δx)+1)-(2^2-2+1) / Δx

Answer 24

Ok you're good till here. From here, what did you do?

Answer 25

then i have

Answer 26

i missed a (

Answer 27

(4+4(Δx)+(Δx)^2)-2-Δx+1)- 3 / Δx

Answer 28

i simplified the right side. it made it seem easier for me.

Answer 29

very good!

Answer 30

Now, from here, how do you continue?

Answer 31

i get 4(Δx)+(Δx)^2-2-Δx / Δx

Answer 32

Ok but look, you have to separate the terms that look alike. For example, here's what I will do to simplify the numbers. I will look at the equation which looks like this\[\frac{((4+4 \Delta x+ \Delta x^2)-2-\Delta x+1)-3}{\Delta x}\]And i will pick out the numbers and I can see I have 4, (-2) and 1 and (-3). So I add them all up. Which gives me,

4-2+1-3=0

And this will remove all the numbers and leave out,\[\frac{(4 \Delta x+ \Delta x^2)-\Delta x}{\Delta x}\]Now remember, the 4 infront of Δx means we have 4 Δx-es. And in the equation there's another Δx that is being subtracted. What do you do?

Answer 33

oh my gosh i totally messed up on the easy eliminating part. lol

Answer 34

i forgot to take out the -2 lol

Answer 35

Heh, no biggie. What's your progress to now?

Answer 36

now i factor out Δx from the numerator and cancel it out with the denominator

Answer 37

i get (Δx)(4+Δx-1) /Δx = 4+Δx-1

Answer 38

opps

Answer 39

Yes very good.. but are you forgeting something?

Answer 40

i messed up. again lol.

Answer 41

=3+Δx!!!

Answer 42

Heheyy!! Great job qtexpress ;).. nice nickname lol

Answer 43

lol thanks

Answer 44

i just really had trouble figuring out how to start the equation. thanks for clearing that up!

Answer 45

you're welcome, don't worry about that. it gets easier when you work with them for a while.

Answer 46

can i show you my next question and you can tell me if i wrote the start of it correctly?