Question

use the four step process fo find f1(x) and then find f1(1), f1(2) and f1(3)....... f(x)= 8x/4+x

Answer 1

what does f1(x) mean?
do you mean f(1)?

Answer 2

no it sort of looks like f ' (x), f ' (1) and so on

Answer 3

ok then that means derivative
f(x) = 8x/4 + x = 2x + x =3x have i written f(x) right or it is some thing else?

Answer 4

Yes but this is telling me something about using this equation to find f '(x) = f(x+h)-f(x)/h

Answer 5

if f(x) is 3x then then the derivative i.e f '(x) is 3
else you can use the formula which is that derivative (f '(x) ) is given by
\[f \prime(x) = \lim_{h \rightarrow 0}\frac{ f(x+h) - f(x) }{ h } \]
now can you find f '(x) ?

Answer 6

f(x)=\[\frac{ 8x}{4+x}\]

Answer 7

I have to find f ' (x) from that equation you gave me

Answer 8

ok so so far we have been considering f(x) wrong.....
let`s start again then.....
can you tell me what is f(x+h)?

Answer 9

I don't know...okay ive confused you! My problem is : use the four step process to find f ' (x) and then find f ' (1), f ' (2), f ' (3). f(x)=\[\frac{ 8x}{4+x}\]

Answer 10

I was just assuming that in order to find f ' (x) we had to use the equation that you gave with the f(x+h)-f(x)/h

Answer 11

in that process your 1st step still is f(x+h)
do you know how to calculate it or not?

Answer 12

www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip1-5.pdf
check this out .....it will help you out a bit in getting hold of method

Answer 13

I dont know how to calculate that and I cant seem to find any examples to show me the way

Answer 14

ok f(x) = 8x/(4+x)
now to calculate f(x+h) all you nees is put x + h instead of x
so
f(x+h) = 8(x+h)/(4+(x+h ))

Answer 15

2nd step : tell what is f(x+h) - f(x)
i.e f(x+h) - f(x) = ?

Answer 16

8x+8h/4x+4h=2x+2h ?

Answer 17

no what i`ll do is now give you step by step solution and you try to understand each step (why this step?)
ok

Answer 18

f(x) = 8x/(4+x)

f(x+h) = 8(x+h)/ (4 + (x+h))
clear till now?

Answer 19

okay, thank you

Answer 20

I understand the equation just not how to solve it, yes

Answer 21

ok cool
now f(x+h) - f(x) = 8(x+h)/ (4 + (x+h)) - 8x/(4+x)
taking common denominator and simplifying we get
f(x+h) - f(x) = 32h/(4+x)(4+x+h)

clear till now?

Answer 22

yes

Answer 23

cool
3rd step was to take out common factor h from this expression
so can you see that we have already obtained that
in numerator 32h = 32(h) ?
clear till now?

Answer 24

yes, got it

Answer 25

ok now putting the things in the above mentioned formula
f '(x) = [ 32h/(4+x)(4+x+h) ] / h
cancelling common factors
32/(4+x)(4+x+h)

now taking the limit h tending to zero for the above expression we get
f '(x) = 32/(4+x)(4+x)
= 32/(4+x)^2

Answer 26

final answer
\[f \prime (x) = \frac{ 32 }{ (4+x)^{2} }\]

Answer 27

alright, and that is the formula I use to find the other 3 answers?

Answer 28

yes this is the general formula for all x expect -4 beacause it`s not in domain of the function

Answer 29

also i appologize for the late reply we had a unexpected network failure....

Answer 30

so f ' (1) = 1.28?

Answer 31

yes!!

Answer 32

Thats okay I appreciate you helping me out!

Answer 33

my pleasure
so finally you trough with the question or still some confusion?