## hashsam1 3 years ago 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

1. RolyPoly

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

2. hashsam1

left hand limit and right hand ljmits arent like the derivatives

3. RolyPoly

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

4. RolyPoly

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.