March 26th, 2018, 10:13 AM  #11 
Senior Member Joined: May 2016 From: USA Posts: 1,053 Thanks: 431  
March 27th, 2018, 03:53 AM  #12 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 232 Thanks: 2  
March 27th, 2018, 04:39 AM  #13 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,248 Thanks: 887  "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: 1,053 Thanks: 431  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. 

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