2. (MGSE9-12.F.IF.4) Find the Maximum or Minimum of \( g(x)=-x^{2}-2 x+8 \).
A. maximum of \( (0,8) \)
B. b. minimum of \( (0,8) \)
C. c. maximum of \( (-1,9) \)
D. d. minimum of \( (-1,9) \)

Answer

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Answer

\( \text{Maximum at }(-1, 9)\)

Steps

Step 1 ：\( g'(x)=-2x-2 \)

Step 2 ：\( g'(x)=0 \Rightarrow x=-1 \)

Step 3 ：\( g(x)=-x^2-2x+8 \Rightarrow g(-1)=9 \)

Step 4 ：\( \text{As the coefficient of }x^2\text{ is negative, g(x) has a maximum at }x=-1\)

Step 5 ：\( \text{Maximum at }(-1, 9)\)