Define the right derivative of a function $f$ at $x = a$ to be the following limit if it exists. $\lim _ { h \rightarrow 0 ^ { + } } \frac { f ( a + h ) - f ( a ) } { h }$, where $h \rightarrow 0 ^ { + }$ means $h$ approaches 0 only through positive values. Statements (1) If $f$ is differentiable at $x = a$ then $f$ has a right derivative at $x = a$. (2) $f ( x ) = | x |$ has a right derivative at $x = 0$. (3) If $f$ has a right derivative at $x = a$ then $f$ is continuous at $x = a$. (4) If $f$ is continuous at $x = a$ then $f$ has a right derivative at $x = a$.
Define the right derivative of a function $f$ at $x = a$ to be the following limit if it exists. $\lim _ { h \rightarrow 0 ^ { + } } \frac { f ( a + h ) - f ( a ) } { h }$, where $h \rightarrow 0 ^ { + }$ means $h$ approaches 0 only through positive values.
\textbf{Statements}
(1) If $f$ is differentiable at $x = a$ then $f$ has a right derivative at $x = a$.\\
(2) $f ( x ) = | x |$ has a right derivative at $x = 0$.\\
(3) If $f$ has a right derivative at $x = a$ then $f$ is continuous at $x = a$.\\
(4) If $f$ is continuous at $x = a$ then $f$ has a right derivative at $x = a$.