Which of the following lines is/are parallel to the tangent line of the graph of $y = - x ^ { 3 }$ at the point where $x = 1$ and the slope of the tangent line is $- 3 x ^ { 2 }$ .
(I) y = -3x + 1
(II) y = 3x + 1
(III) y = -3x - 4
(IV) y = 3x + 1
A) (II) and (III)
B) (I) and (III)
C) (I) and (II)
D) (III) and (IV)
E) none of these

Question

Which of the following lines is/are parallel to the tangent line of the graph of $y = - x ^ { 3 }$ at the point where $x = 1$ and the slope of the tangent line is $- 3 x ^ { 2 }$ . 
(I) y = -3x + 1
(II) y = 3x + 1
(III) y = -3x - 4
(IV) y = 3x + 1
A) (II) and (III)
B) (I) and (III)
C) (I) and (II)
D) (III) and (IV)
E) none of these

Quizplus · Accepted Answer

The slope of the tangent line to the graph of $y = -x^3$ at $x = 1$ is given by the derivative, which is $-3x^2$. Substituting $x = 1$ into this derivative gives a slope of $-3$. Lines parallel to this tangent line must also have a slope of $-3$. Among the given options, (I) $y = -3x + 1$ and (III) $y = -3x - 4$ have a slope of $-3$, making them parallel to the tangent line.

Which of the Following Lines Is/are Parallel to the Tangent y=−x3y = - x ^ { 3 }y=−x3

Which of the Following Lines Is/are Parallel to the Tangent $y = - x ^ { 3 }$