Question

@jim_thompson5910

Posting a file

Answer 1

I think its b?

Answer 2

Because it's on the continuous graph, but there is a whole there meaning x cannot equal whatever b is so it's not differential there?

Answer 3

differentiable*

Answer 4

A is also not differentiable.

Answer 5

I would say A, but i could be wrong.

Answer 6

The answer is A because the graph is continuous at that point (there is no jump or hole) but it's a "corner", a sudden change in direction of the graph, meaning it is not differentiable.

Answer 7

I think it's differentiable at b because the limit at b exists. I'll have to think it over though since I'm not 100% sure.

Answer 8

ah, yes. b is not continuous because limit of that point and actual value are not the same

Answer 9

I don't remember how to tell when things are differetiable or not and stuff

Answer 10

true, the function isn't even continuous there, so cross off b

Answer 11

There is a limit, but it isn't differentiable. There is no tangent at b because there is no point.

Answer 12

Oh right there is a whole because as x approaches it from the left and the right it's different right?

Answer 13

a hole*

Answer 14

anywhere you have a sharp point like you have at x = a, is where it's not differentiable

Answer 15

Yeah I remember that much

Answer 16

the same also applies to places where vertical tangent lines occur

Answer 17

But am I right about B? That's why it's not differential because the limit is different from when it approaches from left and right?

Answer 18

Or it is differentiable? Ugh im confused haha

Answer 19

What you're saying applies to D. The limit is the same from both directions at B.

Answer 20

Is it not continuous at B? But B is differentiable? Its not continuous because the limit is different approaching from left and right?

Answer 21

well, question says which is continuous, but not differentiable, and we see that at x=b it is not continuous, so we cross that out.

Answer 22

So B is not continuous because of the hole, but it is differentiable?

Answer 23

it's not continuous because \(\displaystyle \lim_{x\rightarrow b}f(x) \neq f(b)\)

Answer 24

Yeah that's what I said isn't it? The approaching from left and right thing?

Answer 25

A - continuous but not differentiable (corner)
B - discontinuous (hole) and not differentiable (limit /= point)
C - continuous and differentiable
D - discontinuous (jump) and not differentiable (limit from right /= limit from left)
E - continuous and differentiable

Answer 26

Okay.. I just don't get like what an open hole stands for and a close hole etc. I forgot.

Answer 27

in order for it to be differentiable, it needs to be continuous, so at x=b, it is both not continuous and differentiable

Answer 28

Oh okay.

Answer 29

I think... haha

Answer 30

It makes sense.

@jim_thompson5910 I'll open another new question so we can work on the next one.

Answer 31

yeah that sounds familiar, the necessity of it being continuous for it to be differentiable

and ok

Answer 32

yeah, it make sense, just want to make sure though