Problem

Question 8:
(2 marks)
The function \( f(x)=x^{3}+9 x^{2}-48 x-8 \) has relative minimum value at
a) \( (-8,-440) \)
b) \( (2,-60) \)
c) \( (2,60) \)
d) \( (-2,-60) \)

Answer

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Answer

\( (2, -60) \)

Steps

Step 1 ：\( f'(x) = 3x^2 + 18x - 48 \)

Step 2 ：\( f''(x) = 6x + 18 \)

Step 3 ：\( x = 2 \)

Step 4 ：\( f(2) = -60 \)

Step 5 ：\( (2, -60) \)

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