Question

find the difference quotient
f(x) = 4 +3x-x^2
f(3+h) - f(3)/h
please show work

Answer 1

the whole thing is over h

Answer 2

substitute (3+h) and (3) into your function

then divide by h and use algebraic techniques to solve

Answer 3

you end up with 3 - 2x

Answer 4

if you simply want someone to go thru the effort of typing it all out for you so that you can copy it to your homework; im sure someone will oblige ;)

Answer 5

not true, I am taking a class and I just don't understand how to do some of the problems. I am a single mom going back to school and struggling a bit. Thanks for your help.

Answer 6

then at what part does your understanding begin to fade?

Answer 7

im a single dad going back to college.... so that really doesnt apply does it?

Answer 8

suppose we have the function:

f(x) = x+2

How do we determine: f(5) ??

Answer 9

Good for you apparently you are better off then I am. I am just looking for help ok?

Answer 10

or simply put:
f(x=5) ?

Answer 11

You put 5 in for x

Answer 12

thats right :)

then for these that you have we do that same, but with the x=3 and the x=3+h

Answer 13

what do those look like then?

Answer 14

so I will end up with 2 answers?

Answer 15

youll end up subtracting one function from the other ...yes,

4 +3x-x^2

Answer 16

4 +3(3+h)-(3+h)^2 - [4 +3(x)-(3)^2] = ?

Answer 17

ok I understand now

Answer 18

when all that tedious window dressing is done; you should obtain the result; 3+h-2x for an answer :)

Answer 19

do i multiply by h then to get rid of the h on the bottom?

Answer 20

you can simply divide everything by h to get rid of it; since there is no = sign to equate to, we should avoid doing the multiply by 'h'.

Answer 21

it might be correct, but i dont know how accurate it can be :)

Answer 22

ok

Answer 23

4 + 9 + 3h -9 -6h -h^2 - 4 -9 + 81
------------------------------- is what i get so far, if i didnt mess it up
h

Answer 24

gonna have to work it on paper; i get to many typos this way :)

Answer 25

see, 3^2 = 9; not 81 :)

Answer 26

The following expression replaces the x in the function value by (h+3) subtract the result of replacing the x in the function value by 3 and then dividing this result by h.
\[\left(4+3 x-x^2\text{/.}x\to h+3\right)-\frac{\left(4+3 x-x^2\text{/.}x\to 3\right)}{h} \]= \[9+3 (3+h)-(3+h)^2-3 x \]
Although I could be wrong.

Answer 27

4 + 9 + 3h -9 -6h -h^2 - 4 -9 + 9
-------------------------------
h

-3h -h^2 -3h h^2
-------- = ---- - ---- = -3 -h ... but i gotta recheck myself again :)
h h h

Answer 28

3-2x; as x-> 3 we get

3 -6 = -3; ...its good :)

Answer 29

as h-> 0 we get -3 as an answer, right?

Answer 30

now how can i make this clearer? or are we good with it?

Answer 31

robtob; good effort, wrong interpretation of the expression ;)

Answer 32

amistre64,

Blundered on the first post. I think the following is now correct. At 76 years if age I cannot type with the toes of my left foot and monitor what is going on on the computer screen in real time.
\[\left(4+3 x-x^2\text{/.}x\to h+3\right)-\frac{\left(4+3 x-x^2\text{/.}x\to 3\right)}{h}=4-\frac{4}{h}-3 h-h^2 \]

Answer 33

:)

Answer 34

\[\frac{[4 + 3(3+h) - (3+h)^2] - [4+3(3)-(3)^2]}{h}\]

Answer 35

since the original equation is : 4+3x-x^2...it has to derive down to:

3 -2x; and at f(3) that has to equal -3 when h=0

Answer 36

\[\frac{[4+9-9-4+9-9] -3h - h^2}{h}\]

Answer 37

\[\frac{-3h}{h} - \frac{h^2}{h}\] equals:

-3 - h

Answer 38

when h = 0; this is -3 :)

Answer 39

thank you so much for your help, sorry my internet dropped

Answer 40

'sok; internets a fickle beast :)

Answer 41

amistre64,

googled: difference quotient and looked at the first hit.
http://answers.yahoo.com/question/index?qid=20090320184937AAl0VC6

Got the general idea now.

Thanks.

Answer 42

I hope i am not in over my head going back to school and starting with a calc class. This site has been really helpful.