Consider the function $f(x)=-3 x^{2}+30 x-6$ a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range.

Step 1 ：We can complete the square, to get \(f(x) = 96 - 3(x - 5)^2\).

Step 2 ：Thus, the graph of \(f(x)\) is a parabola with axis of symmetry \(x = 5\), so the function has a maximum value.

Step 3 ：The maximum value of the function is \(96\) and it occurs at \(x = 5\).

Step 4 ：The function's domain is all real numbers, and its range is \(-\infty, 96\].

Step 5 ：The smallest possible value of \(c\) is \(\boxed{5}\).