On problems 1-2, determine whether or not the conditions of Rolle's Theorem are met. If the conditions are met, find the value of c that the theorem guarantees. 1. f(x)=x-11x+30 [5,6] 2. f(x)=(x+4)2(x-3) [-4,3] On problems 3-4, determine whether or not the conditions of the Mean Value Theorem are met. If the conditions are met, find the value of c that the theorem guarantees. 3. f(x)=x-x-2x [-1,1] 4. f(x)=2 cosx+cos(2x) [0, 7] (Use your calculator.) You may use your calculator on problems 5-6, but be sure you show supporting work. 5. A trucker handed in a ticket at a toll booth showing that in 2 hours, the truck had covered 159 miles on a toll road on which the speed limit was 65 mph. The trucker was cited for speeding. Why? 6. A marathoner ran the 26.2 mile New York marathon in 2 hours, 12 minutes. Show that at least twice, the marathoner was running at exactly 11 mph.