Problem
Question 7: (2 marks) The function \( f(x)=x^{4}-6 x^{2}-8 \) is concaving up over the interval. a) \( (-1,1) \) b) \( (-\infty,-1) \mathrm{U}(1, \infty) \) c) \( (-\infty,-1) \mathrm{U}(-1,1) \mathrm{U}(1, \infty) \) d) none of them
Solution
Step 1 ：\(f'(x) = 4x^3 - 12x\)
Step 2 ：\(f''(x) = 12x^2 - 12\)
Step 3 ：\(f''(x) \ge 0 \Rightarrow x^2 \ge 1 \Rightarrow x \in (-\infty,-1) \cup (1, \infty)\)
