Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the point
whose coordinates are given.
-
$y = x ^ { 2 }$
$$y = \sqrt { x }$$
A) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - 3 ^ { - } } f ^ { \prime } ( x ) = 1 , f ( x )$ is not differentiable at $x = 1$.
B) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is not differentiable at $x = 1$.
C) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = \frac { 1 } { 2 } , f ( x )$ is not differentiable at $x = 1$.
D) Since $\lim _ { x - 3 ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - 7 ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is differentiable at $x = 1$.

Question

Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the point
whose coordinates are given.
-
$y = x ^ { 2 }$
$$y = \sqrt { x }$$
A) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - 3 ^ { - } } f ^ { \prime } ( x ) = 1 , f ( x )$ is not differentiable at $x = 1$. 
B) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is not differentiable at $x = 1$. 
C) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = \frac { 1 } { 2 } , f ( x )$ is not differentiable at $x = 1$. 
D) Since $\lim _ { x - 3 ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - 7 ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is differentiable at $x = 1$.

Quizplus · Accepted Answer

The Answer of Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the point
whose coordinates are given.
-
$y = x ^ { 2 }$
$$y = \sqrt { x }$$
A) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - 3 ^ { - } } f ^ { \prime } ( x ) = 1 , f ( x )$ is not differentiable at $x = 1$. 
B) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = \frac { 1 } { 2 }$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is not differentiable at $x = 1$. 
C) Since $\lim _ { x - z ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - z ^ { - } } f ^ { \prime } ( x ) = \frac { 1 } { 2 } , f ( x )$ is not differentiable at $x = 1$. 
D) Since $\lim _ { x - 3 ^ { + } } f ^ { \prime } ( x ) = 2$ while $\lim _ { x - 7 ^ { - } } f ^ { \prime } ( x ) = 2 , f ( x )$ is differentiable at $x = 1$.

Compare the Right-Hand and Left-Hand Derivatives to Determine Whether or Not