My Math Forum Differentiable or not

 Real Analysis Real Analysis Math Forum

March 26th, 2018, 10:13 AM   #11
Senior Member

Joined: May 2016
From: USA

Posts: 1,310
Thanks: 550

Quote:
 Originally Posted by Lalitha183 Which one do we take as RHD & LHD? Because to my question, answers are like is differentiable/ has L.H.D but not R.H.D/ has R.H.D but not L.H.D/ Neither L.H.D nor R.H.D.
If f(x) is not continuous when x = 0, is f(x) differentiable when x = 0?

March 27th, 2018, 03:53 AM   #12
Senior Member

Joined: Nov 2015

Posts: 232
Thanks: 2

Quote:
 Originally Posted by JeffM1 If f(x) is not continuous when x = 0, is f(x) differentiable when x = 0?
Every differentiable function is continuous. So, it won't.

March 27th, 2018, 04:39 AM   #13
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Quote:
 Originally Posted by Lalitha183 Which one do we take as RHD & LHD? Because to my question, answers are like is differentiable/ has L.H.D but not R.H.D/ has R.H.D but not L.H.D/ Neither L.H.D nor R.H.D.
"RHD" means "Right hand derivative"- that is, coming toward x from that right (above) so is $\displaystyle \frac{f(x+h)- f(x)}{h}$ with h positive, x+ h> x. "LHD" means "Left hand derivative"- that is, coming toward x from the left (below) so is $\displaystyle \frac{f(x+ h)- f(x)}{h}$ with h negative, x+ h< x.

March 27th, 2018, 06:13 AM   #14
Senior Member

Joined: May 2016
From: USA

Posts: 1,310
Thanks: 550

Quote:
 Originally Posted by Lalitha183 Every differentiable function is continuous. So, it won't.
There you go.

Just remember that although

$\text {Not continuous } \implies \text { not differentiable}$,

$\text {Continuous } \not \implies \text { differentiable.}$

So you must address the existence and continuity of the Newton quotient after you find the function to be continuous. And like all limits, to be continuous, the limit of the Newton quotient must exist and be equal whether approached from left or right.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post ZMD Calculus 0 April 23rd, 2017 05:23 AM Omnipotent Calculus 0 October 4th, 2014 01:46 PM alphabeta89 Real Analysis 4 January 28th, 2012 01:56 AM alphabeta89 Real Analysis 0 January 18th, 2012 02:52 AM SyNtHeSiS Calculus 2 April 29th, 2010 03:08 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top