Let $f ( x ) = x ^ { 3 } - 6 x ^ { 2 }$ Then which of the following is the largest interval, of those listed, for which $f ^ { \prime } ( x ) < 0$ for all x
In that interval?

Question

A) $( 4 , \infty )$
B) $( - \infty , 0 )$
C)(0,4)
D) $( - \infty , 0 ) \cup ( 4 , \infty )$
E) $( - \infty , \infty )$

Quizplus · Accepted Answer

The derivative $f'(x) = 3x^2 - 12x = 3x(x-4)$. It is negative when $x(x-4) < 0$, which occurs in the interval (0,4).

Let f(x)=x3−6x2f ( x ) = x ^ { 3 } - 6 x ^ { 2 }f(x)=x3−6x2

Let $f ( x ) = x ^ { 3 } - 6 x ^ { 2 }$