Question

Given that f(x)= absolute(2x+6)
determine where it is not differentiable?

Answer 1

at the corner

Answer 2

not diff at 0

Answer 3

oh yes it is

Answer 4

nah man it isnt

Answer 5

sure it is

Answer 6

ok

Answer 7

absolute value of 2x + 6 =2x+6 if 2x+6 > 0 i.e if x > -3

Answer 8

and of course it is -2x-6 if x < -3

Answer 9

is continuous at -3, but has a corner there, so not differentiable at -3

Answer 10

-2x-6 if x < -3

Answer 11

yah man

Answer 12

@akileez here is a nice picture of the corner
http://www.wolframalpha.com/input/?i= |2x%2B6|

Answer 13

i am confused on this one now?

Answer 14

ok lets go slow

Answer 15

\[|2x+6|\] is actually a piece-wise defined function, just as
\[|x|\] is

Answer 16

ok gotcha

Answer 17

if what is inside the absolute values sign it positive, then it is just itself. for example if x = 2 then\[ |2\times 2 +6|=2\times 2+6\]

Answer 18

on the other hand if what is in the absolute value sign in negative, it is the opposite of that

Answer 19

ok

Answer 20

I understand absolute vlaue

Answer 21

it's the left and right calc that gets me

Answer 22

for example if x = -5 then
\[|2\times -5+6|=-2\times- 5 - 6\]

Answer 23

ok

Answer 24

in other words
\[|2x+6|=2x+6\] or
\[|2x+6|=-2x-6\]

Answer 25

so you have two different lines, one with slope 2 and the other with slope -2. these are different, and they are your derivatives

Answer 26

finally! that is the right and left side calc correct?

Answer 27

exactly

Answer 28

left being the minus 2x

Answer 29

and where do they change?

Answer 30

great I have it meow!

Answer 31

they change when
\[2x+6>0
\]
\[2x>-6\]
\[x>-3\]

Answer 32

in other words they change at -3, so this function is not differentiable there

Answer 33

dose that mean at -3?

Answer 34

yes

Answer 35

did you look at the picture i sent? you see a corner at -3

Answer 36

why in the left side calc is the 6 a minus? I thought that the only x would change signs?

Answer 37

hold on

Answer 38

it only opened to the home page with no equation, pic or anything else

Answer 39

|x| is x if x >0 and -x if x < 0 ok with that?

Answer 40

yes

Answer 41

this means that
|2x+6| = 2x+6 if 2x+6 > 0 or -2x-6 if 2x+6<0

Answer 42

i just replaced the "x" by "2x+6"

Answer 43

ok with that?

Answer 44

yes i see, so both signs must change - makes sense! thanks!

Answer 45

but of course you have to answer in terms of x, not in terms of 2x+6

Answer 46

so if 2x+6>0 that means x >-3 and that is where this changes from 2x+6 to -2x-6

Answer 47

that is where the slope changes from -2 to 2

Answer 48

and so that is where your function is not differentiable.

Answer 49

gotcha!