The curve y = x $3$ +x $2$ - x has two horizontal tangents. Find the distance between these two horizontal lines.
A) $\frac { 11 } { 9 }$

B) $\frac { 22 } { 27 }$

C) $\frac { 32 } { 27 }$
D) $\frac { 5 } { 3 }$
E) $\frac { 14 } { 9 }$
F) $\frac { 4 } { 3 }$
G) $\frac { 13 } { 9 }$

H) $\frac { 7 } { 3 }$

Question

The curve y = x $3$ +x $2$ - x has two horizontal tangents. Find the distance between these two horizontal lines.
A) $\frac { 11 } { 9 }$

B) $\frac { 22 } { 27 }$

C) $\frac { 32 } { 27 }$ 
D) $\frac { 5 } { 3 }$
E) $\frac { 14 } { 9 }$ 
F) $\frac { 4 } { 3 }$ 
G) $\frac { 13 } { 9 }$

H) $\frac { 7 } { 3 }$

Quizplus · Accepted Answer

To find horizontal tangents, set the derivative y' = 3x^2 + 2x - 1 to 0. Solving 3x^2 + 2x - 1 = 0 gives x = 1/3 and x = -1. Plug these x-values into the original equation to find y-values: y(1/3) = -5/27 and y(-1) = 4. The distance between these y-values is |4 - (-5/27)| = 32/27.

The Curve Y = X 333 +X 222 - X Has Two Horizontal Tangents

The Curve Y = X $3$ +X $2$ - X Has Two Horizontal Tangents