At what value of x does the function $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 9 x$ change from increasing to decreasing?
A)3
B)1
C)4
D) - 3
E)2
F)0
G) - 2
H) - 1

Question

Quizplus · Accepted Answer

The function changes from increasing to decreasing at a local maximum, which occurs where the derivative $f'(x) = 3x^2 - 6x - 9$ is zero and changes sign. Solving $3x^2 - 6x - 9 = 0$ gives $x = 3$ and $x = -1$. Testing intervals around these points, the function changes from increasing to decreasing at $x = 3$.

At What Value of X Does the Function f(x)=x3−3x2−9xf ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 9 xf(x)=x3−3x2−9x

At What Value of X Does the Function $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 9 x$