Question

PLEASE HELP!!! Find and simplify the difference quotient f(x + h) − f(x)/h for the following function. f(x) = 8x^3

Answer 1

Can you find \(f(x+h)\) first?

Answer 2

umm is it 8x^3(x+h) ?

Answer 3

No, what you wrote is \(f(x)\cdot (x+h)\)

Answer 4

\[
f(x+h) = 8(x+h)^3
\]

Answer 5

But you have to multiply it out.

Answer 6

i forget how to do that when its a power to the third

Answer 7

Can you do it to a power of 2?

Answer 8

\[
8(x+h)^3=8(x+h)^2(x+h)
\]

Answer 9

(8x^2+16xh+8h^2)(x+h)

Answer 10

i think it is drivation formula and we should differentiate that and we'll have
24x^2

Answer 11

This isn't a differentiation problem. He probably hasn't learned derivatives yet, you learn the difference quotient well before that. He needs to do the problem that was asked.

Answer 12

well im a she btw.. haha

Answer 13

Sorry, the name is a little bit hard to tell.... and that picture, well, I never can figure it out with this darn owls! ;) lol

Answer 14

I knew it was a girl.

Answer 15

haha its all good :p

Answer 16

oh.. so sorry.. i don't know that

Answer 17

so anyway whats the next step?

Answer 18

@sara17 Even if you did the derivative, you'd lose the \(h\).

Answer 19

The next step is to multiply out \[
(8x^2+16xh+8h^2)(x+h)
\]

Answer 20

i cant figure that part out

Answer 21

yes but i think that in the end h will omit

Answer 22

8x^3+16x^2h+8xh+8xh+16xh^2+8h^3

Answer 23

??

Answer 24

second and third power of h are insignificant and i think you should divide it by h

Answer 25

i typed in your answer 24x^2 but it said it was wrong

Answer 26

@wio am i right or wrong...

Answer 27

Hold on.

Answer 28

http://www.wolframalpha.com/input/?i=8%28x%2Bh%29%5E3

Answer 29

so ... which one is my answer.. the extended form?

Answer 30

Expanded form.

Answer 31

ugh it says thats wrong too

Answer 32

That isn't the full solution. You need to subtract f(x)

Answer 33

and divide by h.

Answer 34

so i would subtract the expanded form - 8x^3

Answer 35

:
(8(x+h)^3-8x^3)/h
(8x^3+8h^3+8x^2h+8h^2x+16h^2+16hx-8x^3)
8x^3+8h^3+24h^2x+24x^2h-8x^3/h
8h^2+24hx+24x^2
h is unsignificant so
=24x^2

Answer 36

its saying thats not the right answer. can someone just give me the final answer?

Answer 37

the right answer is 8h^2+24hx+24x^2
but since h is come from the limitation concept so we can omit h and write it 24x^2

Answer 38

You are wrong @sara17

Answer 39

It never specifies what \(h\) is.

Answer 40

\[8h^2+24xh+24x^2\]

Answer 41

THANK YOU!

Answer 42

yw

Answer 43

so i'm not wrong that's exactly my answer

Answer 44

@sara17, your answer was wrong because you keep saying that you can "omit h" which is not true at all, for a difference quotient. It isn't a limit, we haven't said anything about what h is, other than it is non-zero.