Consider the function f(x)=-3x²+30x-9. Determine, without graphing, whether the function has a minimum value or a maximum value. Find the minimum or maximum value and determine where it occurs.
(a) Minimum at x=5, f(5)=-34
(b) Maximum at x=5, f(5)=51
(c) Minimum at x=5, f(5)=51
(d) Maximum at x=5, f(5)=-34"