Let $f ( x ) = \lfloor x \rfloor$ Which of the following is true?

A) $f$ is discontinuous at 0.
B) $f$ has 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 $f ( x ) = \lfloor x \rfloor$ Which of the following is true?

A) $f$ is discontinuous at 0.
B) $f$ has 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 floor function $f(x) = \lfloor x \rfloor$ is discontinuous at integer values, including 0, because it jumps from one integer value to the next.

Let f(x)=⌊x⌋f ( x ) = \lfloor x \rfloorf(x)=⌊x⌋ Which of the Following Is True? A)

Let $f ( x ) = \lfloor x \rfloor$ Which of the Following Is True?

A)