f(x) = x² + 12x + 9 has a A) relative maximum at x = -6 B) relative minimum at x = -6 C) relative maximum at x = -12 D) relative minimum at x = -12 E) relative maximum at x = -9

Question

Quizplus · Accepted Answer

The given function simplifies to $f(x) = x^2 + 12x + 9$. To find the critical points, we differentiate: $f'(x) = 2x + 12$. Setting $f'(x) = 0$ gives $x = -6$. To determine if this is a maximum or minimum, we can use the second derivative test: $f''(x) = 2$, which is positive, indicating a relative minimum at $x = -6$.

F(x) = X2 + 12x + 9 Has a

F(x) = X² + 12x + 9 Has a