Question

If f(x) = 3a|4x – 4| – ax, where a is some constant, find f ′(1).

0
not enough information
e
1

Answer 1

hint:

\[\Large f(x) = |x|\]

\[\Large f'(x) = \frac{|x|}{x}\]

this is a rule you memorize but you can derive this rule by breaking up |x| into +x and -x and deriving each piece (think of it as a piecewise function).

notice how f ' (x) is undefined when x = 0, so that means f(x) is not differentiable at x = 0.

Answer 2

so what should i get as the answer?

Answer 3

0 right?

Answer 4

@jim_thompson5910

Answer 5

one sec

Answer 6

do you see how I got f ' (x) ?

Answer 7

yes @jim_thompson5910

Answer 8

Nice c;

Answer 9

so what should i get as the answer?

Answer 10

So if f(x) = 3a*|4x-4| - ax, then

\[\Large f'(x) = \frac{3a|4x-4|}{4x-4}-a\]

Answer 11

what is the value of f ' (1) ?

Answer 12

that derivative needs a little work

Answer 13

I'm referring to what @jim_thompson5910 wrote

Answer 14

oh right, forgot the chain rule

Answer 15

yes

Answer 16

if f(x) = 3a*|4x-4| - ax, then

\[\Large f'(x) = 4*\frac{3a|4x-4|}{4x-4}-a\]

\[\Large f'(x) = \frac{12a|4x-4|}{4x-4}-a\]

Answer 17

what does that give me as a result?
Please hurry i'm at the library and I have to go in 5 minutes Im running out of time :(

Answer 18

@Zarkon @jim_thompson5910

Answer 19

you can work on it when you get more time

you need to find f ' (1) based on what I posted

this here:

\[\Large f'(x) = \frac{12a|4x-4|}{4x-4}-a\]

Answer 20

It's due very soon

Answer 21

so I j ust plug in 1 for x?

Answer 22

@jim_thompson5910

Answer 23

that would give me 11a

Answer 24

Or 0, right?

Answer 25

into f ' (x) and not f(x)

Answer 26

what is 4x - 4 when x = 1

Answer 27

0

Answer 28

can you divide by zero?

Answer 29

can you say something like 2/0 ?

Answer 30

no

Answer 31

@jim_thompson5910

Answer 32

wouldn't that just be equal to 0?

Answer 33

2/0 is undefined

Answer 34

so

\[\Large f'(x) = \frac{12a|4x-4|}{4x-4}-a\]
\[\Large f'(1) = \frac{12a|4*1-4|}{4*1-4}-a\]
\[\Large f'(1) = \frac{12a|0|}{0}-a\]
\[\Large f'(1) = \ \text{Undefined}\]

Answer 35

that's not an answer option:
my options are:
a)0
b)e
c)not enough information
d)1

Answer 36

@jim_thompson5910

Answer 37

for \(a\ne0\) jim_thompson5910's answer is correct


what happens when \(a=0\)

Answer 38

the answer is = to 0?

Answer 39

right...so the answer depends on \(a\)...and we don't know the value of \(a\)

Answer 40

so the answer is not enough information?!

Answer 41

right...we need to know if a is zero or not. So we don't have enough info

Answer 42

:) ok THANK YOU!!!