Problem
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? \[ f(x)=-x^{2}-8 x-12 \]
Solution
Step 1 ：\( \frac{d}{dx} (-x^2 - 8x - 12) = -2x - 8 \)
Step 2 ：\( -2x - 8 = 0 \Rightarrow x = -4 \)
Step 3 ：\( -x^2 - 8x - 12 = 0 \Rightarrow x = -6, -2 \)
