Question

can someone explain the left hand derivative and right hand derivative rules in order to find whether the function is a differentiable function or not

Answer 1

Wouldn't it be something similar to the case for limit?

Answer 2

left hand limit and right hand ljmits arent like the derivatives

Answer 3

\[f'(x)= \lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}\]
^Limit

A function y=f(x) is differentiable on an open interval if it has a derivative at each point of the interval. It is differentiable on a closed interval [a, b] if it is differentiable on the interior (a,b) and if the limits\[f'(x)= \lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}\](Right-hand derivative of at a)
\[f'(x)= \lim_{h \rightarrow 0^-}\frac{f(b+h)-f(b)}{h}\](Left-hand derivative of at b)
exist at the end point

Answer 4

Right-hand and left-hand derivatives may be defined at any point of a function 's domain. Because of ''A function f(x) has a limit as x->c if and only if it has left-hand and right-hand limits there and these one-sided limits are equal'', a function has a derivative if and only if it has left-hand and right-hand derivatives there, and these one-sided derivatives are equal.