Question

The graphs $y=2x^3-4x+2$ and $y=x^3+2x-1$ intersect at exactly 3 distinct points. The slope of the line passing through two of these points

• A. is equal to 4
• B. is equal to 6
• C. is equal to 8
• D. is not unique

Answer 1

Answer: (C)

is equal to 8

Given equation of curves
$y=2x^3-4x+2$
$y=x^3+2x-1$
Let $(x_1,y_1)$ be a point of intersection of the curves.
$\Rightarrow y_1=2x_1^3-4x_1+2$
And $y_1=x_1^3+2x_1-1$
$\Rightarrow y_1=8x_1-4$
Let $(x_2,y_2)$ be another point of intersection of the curves.
$\Rightarrow y_2=2x_2^3-4x_2+2$
And $y_2=x_2^3+2x_2-1$
$\Rightarrow y_2=8x_2-4$
Now, slope $=\frac{y_2-y_1}{x_2-x_1}$
$\Rightarrow m=\frac{8(x_2-x_1)}{x_2-x_1}$
$\Rightarrow m=8$