Find all the critical numbers of the function $f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } + 1$ .
A) 0, 1, -1
B) -1
C) $\frac { 1 } { 2 }$
D) None

Question

Quizplus · Accepted Answer

Critical numbers of a function occur where its derivative is zero or undefined. For $f(x) = -2x^4 + 4x^2 + 1$, the derivative $f'(x) = -8x^3 + 8x$. Setting $f'(x) = 0$ gives $-8x(x^2 - 1) = 0$, which has solutions at $x = 0, x = 1$, and $x = -1$.

Find All the Critical Numbers of the Function f(x)=−2x4+4x2+1f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } + 1f(x)=−2x4+4x2+1

Find All the Critical Numbers of the Function $f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } + 1$