the-following-formulas-for-faf-primeleftarightfa-and-fafprimeleftarightfa-repres

Question

The following formulas for $f_{-}^{\prime}\left(a ight)$ and $f_{+}^{\prime}\left(a ight)$ represent the left- and right-sided derivatives of a function at a point $a$ , respectively:

$f_{-}^{\prime}\left(a ight)={\displaystyle\lim_{h o0^{-}}{\frac{f(a+h)-f(a)}{h}}}$ , $f_{+}^{\prime}\left(a ight)={\displaystyle\lim_{h o0^{+}}{\frac{f(a+h)-f(a)}{h}}}$

Consider $f (x) = {\begin{matrix} 6 - x^{2} if x \leq 2 \\ 3 x - 4 if x > 2 \end{matrix}$ . Find $f_{-}^{\prime}\left(a ight)$ and $f_{+}^{\prime}\left(a ight)$ at $a equals 2$ .

Accepted Answer

$f_{-}^{\prime}\left(2\right)=-4$

$f_{+}^{\prime}\left(2\right)=3$

Answer

$f_{-}^{'} (2) = - 4$

$f_{+}^{'} (2) = - 3$

Answer

$f_{-}^{'} (2) = - 4$

$f_{+}^{'} (2) = 3$

Answer

$f_{-}^{'} (2) = - 4$

$f_{+}^{'} (2) = 3$