Room for Yuvraj and robjohn

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Jack Rod

03:01

@robjohn hi sir

Jack Rod

03:15

questiin is f(x) is such that =max(x^4,x^3,1/81) i need to find sum of square of reciprocal of the value of x where fx is non differentiable

like i find the graph but it is like unbounded sir

robjohn

03:41

But it is differentiable on the unbounded part.

where is the function non-differentiable?

Jack Rod

from 0to infinity

it is the domain of x

can you show the graph of maximum of this

@robjohn

y=1/81 would be a line parallel to x-axis

there are only two-point one is 1/9 and other is 1 can you confrim this

Jack Rod

04:14

@robjohn hi sir

4 hours later…

robjohn

08:15

There are $3$ points. $-\frac13,1,\frac1{81^{1/3}}$

Jack Rod

no sir only two

@robjohn

robjohn

which of the three are wrong?

Jack Rod

two are wrong

-1/3 and the last one

@robjohn

robjohn

I have plotted the function to be sure, and those points are non-differentiable

There are angles (non-smooth points) in the plot

Jack Rod

can you upload the pic sir

@robjohn

robjohn

08:31

Those definitely look non-differentiable to me

Jack Rod

indeed sir i made a wild guess like my friend

sir i have few more questions

like i was given f(x)=(x-4)^4(x-2)^3(x-1)^2

is there any easy way to find fx instead of multiplying

robjohn

How is multiplication hard?

Jack Rod

not hard i know i can expand it

but is there any other way?

robjohn

what do you want out of it?

I can't figure out anything without knowing what information you want

Do you want a polynomial written as $a_nx^n+a_{n-1}x^{n-1}+\dots$? what is it you want?

As it stands $(x-4)^4(x-2)^3(x-1)^2$ is simple

Jack Rod

leave that sir

sir if fx is differentiable what we can predict about f^2x

assume the example of modulus of x

@robjohn

robjohn

08:46

the chain rule says that $(f^2)'=2ff'$ so $f^2$ is differentiable

Jack Rod

what about fx into modulus of fx

robjohn

by modulus, do you mean the absolute value? the modulus usually refers to the number theory mod function

$|x|$?

Jack Rod

yes

17 secs ago, by robjohn

$|x|$?

robjohn

Use the chain rule. $|f|$ is differentiable anywhere $f$ is differentiable and where $f(x)$ has a value where $|x|$ is differentiable.

So if $f$ is differentiable, we need to look at where $|x|$ is differentiable

where is $|x|$ differentiable?

Jack Rod

everywhere except zero

@robjohn

robjohn

08:55

So, where does the chain rule say that $|f(x)|$ is differentiable (or not)?

Jack Rod

i draw the graph

robjohn

the chain rule...

this is a composition of functions, so the chain rule is indicated.

Jack Rod

my friend say where we see the function is approaching a sharp peak like a triangle function is non differentiable at that peak\

robjohn

where are the points where $|f(x)|$ is not differentiable?

How can one find them?

Jack Rod

12 mins ago, by robjohn

Use the chain rule. $|f|$ is differentiable anywhere $f$ is differentiable and where $f(x)$ has a value where $|x|$ is differentiable.

you said

robjohn

09:03

and knowing what you know about $|x|$, where might $|f(x)|$ not be differentiable?

Jack Rod

it is differentiable everyhwere

robjohn

suppose $f(x)=\sin(x)$ is $|f(x)|$ differentiable everywhere?

Jack Rod

except zero to above one

yes

20 secs ago, by robjohn

suppose $f(x)=\sin(x)$ is $|f(x)|$ differentiable everywhere?

robjohn

really?

Jack Rod

oh wait sorry it is modulus so it is not differentiable at pi,2p,3pi

robjohn

09:09

Jack Rod

yes sir

robjohn

So where is $|f(x)|$ not differentiable?

Jack Rod

@robjohn

0 pi 2pi 3pi

@robjohn

robjohn

In general, where is $|f(x)|$ possibly not differentiable?

Where might $\left|\sin(x)-\frac13\right|$ be non-differentiable?

what can you say about the $x$ where $|f(x)|$ is not differentiable?

ah, I'm speaking to myself.

Jack Rod

09:34

sorry sir there was a power cut

@robjohn extremely sorry sir

if you feel in that way

robjohn

10:00

so back to where we were

39 mins ago, by robjohn

In general, where is $|f(x)|$ possibly not differentiable?

@JackRod I just didn't think I'd get any answer questioning an empty room.

robjohn

11:05

so to finish this up, I'll answer my question: the points where $|f(x)|$ might not be differentiable are where $f(x)=0$.

Jack Rod

11:23

But sir that is not a common case taking them example of -modulus of x we get one more additional point which is origin where f is not differentiable

Sorry sir I see that when I just leaved the rook for the work you have entered three is gap of 30minutes between me you

I admit that this time I myself left the room because I was solving the paper

I have no intention to disrespect after all you are helping me more than you can a request if you read my message just give me text like hi so that I can confirm that you are there and I won't live the room untill you reply

Jack Rod

11:47

@robjohn

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