A. Over what interval is \( f(x) \) increasing?
B. Over what interval is \( f(x) \) decreasing?
C. What are the \( x \)-intercepts of the function \( f(x) \) ?
D. When is \( f(x) \) positive?
E. When is \( f(x) \) negative?
\[
f(x)=-x^{2}-8 x-12
\]

Answer

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Answer

\( -x^2 - 8x - 12 = 0 \Rightarrow x = -6, -2 \)

Steps

Step 1 ：\( \frac{d}{dx} (-x^2 - 8x - 12) = -2x - 8 \)

Step 2 ：\( -2x - 8 = 0 \Rightarrow x = -4 \)

Step 3 ：\( -x^2 - 8x - 12 = 0 \Rightarrow x = -6, -2 \)