Let the function $$f ( x ) = \left\{ \begin{array} { l l l }
\frac { 2 x + 1 } { x } & \text { if } & x < 0 \\
x ^ { 2 } - 4 x + 3 & \text { if } & x \geq 0
\end{array} \right.$$ a) ( 0.75 points) Study the continuity of $f ( x )$ in $\mathbb { R }$. b) ( 0.25 points) Is $f ( x )$ differentiable at $x = 0$ ? Justify your answer. c) ( 0.75 points) Calculate, if they exist, the equations of its horizontal and vertical asymptotes. d) ( 0.75 points) Determine for $x \in ( 0 , \infty )$ the point on the graph of $f ( x )$ where the slope of the tangent line is zero and obtain the equation of the tangent line at that point. At the point obtained, does $f ( x )$ achieve any relative extremum? If so, classify it.
Let the function
$$f ( x ) = \left\{ \begin{array} { l l l }
\frac { 2 x + 1 } { x } & \text { if } & x < 0 \\
x ^ { 2 } - 4 x + 3 & \text { if } & x \geq 0
\end{array} \right.$$
a) ( 0.75 points) Study the continuity of $f ( x )$ in $\mathbb { R }$.\\
b) ( 0.25 points) Is $f ( x )$ differentiable at $x = 0$ ? Justify your answer.\\
c) ( 0.75 points) Calculate, if they exist, the equations of its horizontal and vertical asymptotes.\\
d) ( 0.75 points) Determine for $x \in ( 0 , \infty )$ the point on the graph of $f ( x )$ where the slope of the tangent line is zero and obtain the equation of the tangent line at that point. At the point obtained, does $f ( x )$ achieve any relative extremum? If so, classify it.