Let $f ( x ) = \left\{ \begin{array} { c c }
x ^ { 2 } & x \leq 0 \
- x ^ { 2 } & x 0
\end{array} \right.$ Which of the following is true?

A) $f$ is discontinuous at 0.
B) $f$ does not have a derivative at 0.
C) $f$ has a corner at (0,0).
D) $f$ has a has a horizontal tangent line at (0,0).
E) $f$ has a vertical tangent line at (0,0).

Question

Let $f ( x ) = \left\{ \begin{array} { c c } 
x ^ { 2 } & x \leq 0 \
- x ^ { 2 } & x > 0
\end{array} \right.$ Which of the following is true?

A) $f$ is discontinuous at 0.
B) $f$ does not have a derivative at 0.
C) $f$ has a corner at (0,0).
D) $f$ has a has a horizontal tangent line at (0,0).
E) $f$ has a vertical tangent line at (0,0).

Quizplus · Accepted Answer

The Answer of Let $f ( x ) = \left\{ \begin{array} { c c } 
x ^ { 2 } & x \leq 0 \
- x ^ { 2 } & x > 0
\end{array} \right.$ Which of the following is true?

A) $f$ is discontinuous at 0.
B) $f$ does not have a derivative at 0.
C) $f$ has a corner at (0,0).
D) $f$ has a has a horizontal tangent line at (0,0).
E) $f$ has a vertical tangent line at (0,0).

Let f(x)={x2x≤0−x2x>0f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & x \leq 0 \\- x ^ { 2 } & x > 0\end{array} \right.f(x)={x2−x2​x≤0x>0​

Let $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & x \leq 0 \\- x ^ { 2 } & x > 0\end{array} \right.$