On the coordinate plane, consider the graphs of two functions $f(x) = x^{5} - 5x^{3} + 5x^{2} + 5$ and $g(x) = \sin\left(\frac{\pi x}{3} + \frac{\pi}{2}\right)$ (where $\pi$ is the circumference ratio). Select the correct options. (1) $f'(1) = 0$ (2) $y = f(x)$ is increasing on the closed interval $[0, 2]$ (3) $y = f(x)$ is concave up on the closed interval $[0, 2]$ (4) For any real number $x$, $g(x + 6\pi) = g(x)$ (5) Both $y = f(x)$ and $y = g(x)$ are increasing on the closed interval $[3, 4]$
On the coordinate plane, consider the graphs of two functions $f(x) = x^{5} - 5x^{3} + 5x^{2} + 5$ and $g(x) = \sin\left(\frac{\pi x}{3} + \frac{\pi}{2}\right)$ (where $\pi$ is the circumference ratio). Select the correct options.\\
(1) $f'(1) = 0$\\
(2) $y = f(x)$ is increasing on the closed interval $[0, 2]$\\
(3) $y = f(x)$ is concave up on the closed interval $[0, 2]$\\
(4) For any real number $x$, $g(x + 6\pi) = g(x)$\\
(5) Both $y = f(x)$ and $y = g(x)$ are increasing on the closed interval $[3, 4]$