Determine all values of , (if any), at which the graph of the function has a horizontal tangent.
$y ( x ) = x ^ { 4 } - 4 x + 4$
A) $x = 1$
B) $x = 0$ and $x = - 1$
C) $x = 0$ and $x = 1$
D) $x = 0$
E) The graph has no horizontal tangents.

Question

Quizplus · Accepted Answer

To find where the graph of the function $y(x) = x^4 - 4x + 4$ has a horizontal tangent, we need to find where its derivative $y'(x)$ equals 0. The derivative is $y'(x) = 4x^3 - 4$. Setting this equal to 0 gives $4x^3 - 4 = 0$, or $x^3 = 1$, which has the solution $x = 1$.

Determine All Values of , (If Any), at Which the Graph