On problems 1-2, determine whether or not the conditions of Rolle's Theorem are met. If the...

 

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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. 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.

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1 To determine if the conditions of Rolles Theorem are met for fx x2 11x 30 on the interval 56 we need to check if the function is continuous on the c... View the full answer