Find all critical numbers for the function $f ( x ) = x ^ { 3 } - 12 x ^ { 2 }$ .
A)0
B)0, 8
C)0, 4
D)No Critical Number
E)8
F)1, -1
G)4
H)None of the above

Question

Quizplus · Accepted Answer

Critical numbers occur where the derivative of the function equals zero or is undefined. For $f(x) = x^3 - 12x^2$, the derivative is $f'(x) = 3x^2 - 24x$. Setting this equal to zero gives $3x^2 - 24x = 0$, which simplifies to $x^2 - 8x = 0$ or $x(x - 8) = 0$. Thus, the critical numbers are $x = 0$ and $x = 8$.

Find All Critical Numbers for the Function f(x)=x3−12x2f ( x ) = x ^ { 3 } - 12 x ^ { 2 }f(x)=x3−12x2

Find All Critical Numbers for the Function $f ( x ) = x ^ { 3 } - 12 x ^ { 2 }$