Question

Find the difference quotient for f(x)=12/x^2
Any help is greatly appreciated.

Answer 1

\[f(x)=\frac{ 12 }{ x^2 } \]

Answer 2

Im still struggling with this one I just dont get it please help!

Answer 3

\[\frac{\frac{12}{(x+h)^2}-\frac{12}{x^2}}{h}\]

Answer 4

:) that is exactly where I am stuck.....

Answer 5

\[\frac{\frac{12x^2}{(x+h)^2*x^2}-\frac{12(x+h)^2}{(x+h)^2x^2}}{h}\]=
\[\frac{12x^2-(x^2+2xh+h^2)}{h(x+h)^2x^2}\]=
\[\frac{11x^2-2xh-h^2}{h(x+h)^2x^2}\]

Answer 6

do you need to take the limit?

Answer 7

woops sec I messed up

Answer 8

interesting so you did multiplied side by side.... and I think I need the limit. Which I believe is the simplest form?

Answer 9

\[\frac{12x^2-12(x^2+2xh+h^2)}{hx^2(x+h)^2}\]=
\[\frac{12x^2-12x^2-24xh-12h^2}{hx^2(x+h)^2}\]=
\[\frac{-24xh-12h^2}{hx^2(x+h)^2}\]=
\[\frac{-24-12h}{x^2(x+h)^2}\]

Answer 10

when I say limit, I mean when h goes to infinity. Is this for calculus or algebra?

Answer 11

Alg

Answer 12

I mean 0 not infinity

Answer 13

ok well then you don't want the limit im guessing.

Answer 14

this is the form you want.

Answer 15

you are actually doing calculus you just don't know it yet:)

Answer 16

God i can only imagine the rest....

Answer 17

either way I chose this path so better get used to it :) one last question... Is this the simplest form I am looking at other exmaples and they're nice and neat

Answer 18

Out of all this one was vicious

Answer 19

\[\frac{-24x-12h}{x^2(x+h)^2}\]

Answer 20

that's the final

Answer 21

K K thank you so much I will try to sort the others by myself... :) looks like another all nighter. Thanks again

Answer 22

yeah there is not much else you can do to it
http://www.wolframalpha.com/input/?i=simplify++%28%E2%88%9224x%E2%88%9212h+%29%2F%28x%5E2*%28x%2Bh%29%5E2%29++++

Answer 23

nice. Will check this site little bit more.