Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x =

A)-3
B)-2
C)-1
D)0
E)2

Name: Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x = A)-3 B)-2 C)-1 D)0 E)2
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Question

Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$ Then ƒ has a relative minimum at x =

A)-3
B)-2
C)-1
D)0
E)2

Quizplus · Accepted Answer

The derivative of f(x) is f'(x) = -3x^2 - 12x - 9. Setting f'(x) = 0 and solving for x gives x = -3. Since f''(-3) = 18 > 0, f(x) has a relative minimum at x = -3.

Let f(x)=−x3−6x2−9x+1f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1f(x)=−x3−6x2−9x+1

Let $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } - 9 x + 1$