At how many different values of x does the curve y = x $3$ - 2x have a tangent line parallel to the line $y = x$ ?
A)0
B)1
C)2
D)3
E)4
F)5
G)6
H)7

Question

Quizplus · Accepted Answer

To find where the curve has a tangent line parallel to $y = x$, we need to set the derivative of $y = x^3 - 2x$ equal to the slope of $y = x$, which is 1. The derivative of $y = x^3 - 2x$ is $3x^2 - 2$. Setting this equal to 1 gives $3x^2 - 2 = 1$, which simplifies to $3x^2 = 3$, and further to $x^2 = 1$. Solving for $x$ gives $x = \pm1$, so there are 2 values of $x$ where the curve has a tangent line parallel to $y = x$.

At How Many Different Values of X Does the Curve 333

At How Many Different Values of X Does the Curve $3$