For a constant $a$ ($a \neq 3\sqrt{5}$) and a quadratic function $f(x)$ with negative leading coefficient, the function $$g(x) = \begin{cases} x^{3} + ax^{2} + 15x + 7 & (x \leq 0) \\ f(x) & (x > 0) \end{cases}$$ satisfies the following conditions. (가) The function $g(x)$ is differentiable on the set of all real numbers. (나) The equation $g'(x) \times g'(x - 4) = 0$ has exactly 4 distinct real roots. What is the value of $g(-2) + g(2)$? [4 points] (1) 30 (2) 32 (3) 34 (4) 36 (5) 38
For a constant $a$ ($a \neq 3\sqrt{5}$) and a quadratic function $f(x)$ with negative leading coefficient, the function
$$g(x) = \begin{cases} x^{3} + ax^{2} + 15x + 7 & (x \leq 0) \\ f(x) & (x > 0) \end{cases}$$
satisfies the following conditions.\\
(가) The function $g(x)$ is differentiable on the set of all real numbers.\\
(나) The equation $g'(x) \times g'(x - 4) = 0$ has exactly 4 distinct real roots.\\
What is the value of $g(-2) + g(2)$? [4 points]\\
(1) 30\\
(2) 32\\
(3) 34\\
(4) 36\\
(5) 38