(C) $x=\frac{29 \sin 61^{\circ}}{\sin 79^{\circ}}$
(D) $x=\frac{21 \sin 40^{\circ}}{\sin 79^{\circ}}$
9 Let $f(x)=x^{3}-\left(k^{2}-4\right) x+1$
For which of the values of $k$ below is $f(x)$ many-to-one?
(A) $k=2$
(B) $k=-2$
(C) $k=1$
(D) $k=-4$

Answer

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Answer

Final Answer: $\boxed{1}, \boxed{-4}$

Steps

Step 1 ：Find the derivative of the function: $f'(x) = 3x^2 - (k^2 - 4)$

Step 2 ：Find the critical points: $x = \pm\frac{\sqrt{3k^2 - 12}}{3}$

Step 3 ：Check for which values of k there are multiple critical points: $k = 1, -4$

Step 4 ：Final Answer: $\boxed{1}, \boxed{-4}$