Let $f ( x ) = - x ^ { 2 }$ 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 $f ( x ) = - x ^ { 2 }$ 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 function $f(x) = -x^2$ is a continuous and differentiable function everywhere on the real number line. At $x = 0$, the derivative $f'(x) = -2x$ equals 0, indicating a horizontal tangent line at the point (0,0), making option D correct.

Let f(x)=−x2f ( x ) = - x ^ { 2 }f(x)=−x2

Let $f ( x ) = - x ^ { 2 }$