Question

If f(x)= 2a|3x – 9| – ax, where a is some constant, find f ′(3).

Answer 1

ok there are 2 cases 1 case is that the absolute is - and the othere is that its +

Answer 2

a. 0
b. DNE
c. 1
d. not enough information

Answer 3

i have no idea wht u mean

Answer 4

@iambatman @eliassaab @Michele_Laino

Answer 5

they're asking for f' the derivative right?

Answer 6

yes

Answer 7

where we subs. 3 for x

Answer 8

i just dont know how to do it because when we first find the derivative of x its a single x the x turns into a 1

Answer 9

@ganeshie8 @eliassaab please help

Answer 10

@wio

Answer 11

\[\frac{ d }{ dx }\left| f \left( x \right) \right|=\frac{ f \left( x \right) }{ \left| f \left( x \right) \right| }f \prime \left( x \right)\]

Answer 12

i dont understand

Answer 13

\[f \prime \left( x \right)=2a \frac{ 3x-9 }{ \left| 3x-9 \right| }*3-a\]

Answer 14

have you followed?

Answer 15

doing it rn

Answer 16

2a * 3-a

Answer 17

???

Answer 18

it is not derivable at x=3
because denominator is zero

Answer 19

ohh so dne

Answer 20

but wait

Answer 21

wht about the a's doesnt it make this equation not solvable because we dont know wht the value of a is?

Answer 22

@surjithayer

Answer 23

no \[\left| x \right| ~is~continuous~at~x=0~but~\not~derivable~at ~x=0\]
\[\left| x-a \right|~is~continuous~but~\not~derivable~at~x=a,whre~a~is~a~constant.\]

Answer 24

so it dne?

Answer 25

@surjithayer

Answer 26

yes,correct
because 3x-9=3*3-9=0

Answer 27

but zero is also an answer

Answer 28

a. 0
b. DNE
c. 1
d. not enough information

Answer 29

i have shown you \[\left| f \left( x \right) \right|=0~at~x=3\]

Answer 30

so option b is correct as you have mentioned.

Answer 31

thanks for the help :)

Answer 32

yw

Answer 33

if a=0 though
then f(x)=0
we don't know what a is

Answer 34

so when a is not equal to zero then f'(3) dne

Answer 35

i'm saying I think we don't have enough information