The minimal value of the function y = x4 - 4x3 + 16x is at
A) -1
B) 2
C) -2
D) 1

Question

Quizplus · Accepted Answer

To find the minimal value of the function $y = x^4 - 4x^3 + 16x$, we first find its derivative: $y' = 4x^3 - 12x^2 + 16$. Setting the derivative equal to zero to find critical points gives $4x^3 - 12x^2 + 16 = 0$. Factoring out 4 gives $x^3 - 3x^2 + 4 = 0$, which is not easily solvable without specific techniques or tools. However, by inspection or using a graphing approach, we can identify that $x = 2$ is a critical point. Further analysis or using the second derivative test can confirm that this point corresponds to a local minimum. Therefore, the minimal value of the function occurs at $x = 2$.

The Minimal Value of the Function Y = X4 -