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anonymous
 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
anonymous
 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

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Wouldn't it be something similar to the case for limit?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0left hand limit and right hand ljmits arent like the derivatives

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[f'(x)= \lim_{h \rightarrow 0}\frac{f(x+h)f(x)}{h}\] ^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\[f'(x)= \lim_{h \rightarrow 0^+}\frac{f(a+h)f(a)}{h}\](Righthand derivative of at a) \[f'(x)= \lim_{h \rightarrow 0^}\frac{f(b+h)f(b)}{h}\](Lefthand derivative of at b) exist at the end point

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Righthand and lefthand 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 lefthand and righthand limits there and these onesided limits are equal'', a function has a derivative if and only if it has lefthand and righthand derivatives there, and these onesided derivatives are equal.
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