If Bob is driving along a toll road and passes the first toll reader at 12:00 and is traveling 50 miles an hour, he then passes the second reader 10 miles later at 12:10. Using the Mean Value Theorem, can you find Bob's average speed? Can you prove that he must have been driving faster than 55 miles per hour at some point? O Bob's average speed was 50 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers. O Bob's average speed was 50 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers. O Bob's average speed was 60 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers. O Bob's average speed was 60 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.David is 1 year old and he climbs off a couch that is 2 feet high and lands on the floor. It takes him 1 second to get off the couch. Assuming David's height off the floor is continuous and differentiable, which of the following is true? f( 1 ) - f(0) The Mean Value Theorem applies; the average rate of change is: = 2 ft/ sec f(1 ) - f(0) O The Mean Value Theorem applies; the average rate of change is: = 1 = 1ft/ sec O The Mean Value Theorem does not apply. f(1 ) - f(0) The Mean Value Theorem applies; the average rate of change is: = -IN = 2 ft/ secLet f(x) = x2 - 2x. Use Rolle's Theorem to find all the values of x = c in the interval [0, 2] such that f '(c) = 0. O C= 0 O C= 3 O c= 1 O c = 1.5Let f(x) = tan(x). Use Rolle's Theorem to find all the values of x = c in the interval [0, / ] such that f '(c) = 0. O f(x) = tan(x) is not continuous on [0, / ], or differentiable on (0, / ),so Rolle's Theorem cannot be applied. O C= O c= 1 O C=0Which of the following is true? O If the Mean Value Theorem is applied then Rolle's Theorem is automatically applicable. O If Rolle's Theorem can be applied it is possible that the Mean Value Theorem cannot be applied. O The Mean Value Theorem is a special case of Rolle's Theorem. O Rolle's Theorem is a special case of the Mean Value Theorem