26. Let \( f(x)=-3 \cos x+3 \) The maximum value attained by \( f \) on the closed internal \( [0,2 \pi] \) oecurs when \( x \) is equal to \( \begin{array}{llll}\text { A. }-3 & \text { B. } 0 & \text { C. } \frac{\pi}{2} & \text { D, } \%\end{array} \)

To find the maximum value of the function \( f(x) = -3 \cos x + 3 \), we need to analyze the cosine function. The cosine function has a maximum value of 1, hence \( f(x) \) reaches its maximum when \( \cos x \) is at its minimum, which is -1. This occurs when \( x = \pi \). Thus, the maximum value of \( f(x) \) is \( -3(-1) + 3 = 6 \). When looking at the choices provided, none of them directly correspond to \( x = \pi \), but it’s essential to note that the maximum value attained by \( f \) on the closed interval \( [0, 2\pi] \) occurs at \( x = \pi \). Also, \( f \) achieves its minimum value when \( \cos x = 1 \), which occurs at \( x = 0 \) or \( x = 2\pi \), giving a minimum of \( f(0) = f(2\pi) = 0 \). So \( f(x) \) swings between 0 and 6 on the interval \( [0, 2\pi] \).