If f(x) = 3x2 + 2x, does the Mean Value Theorem apply on the interval [0, 1] and why? O The Mean Value Theorem applies because f(x) is differentiable on the open interval (0,1). O The Mean Value Theorem applies because, f(x) is differentiable on the closed interval [0, 1]. O The Mean Value Theorem does not apply because f(x) is not continuous on the closed interval [0, 1]. O The Mean Value Theorem applies because f(x) is continuous on [0, 1].For the function f(x) = sin(x), on the interval [0, / ], which of the following is true? O For f(x) = sin(x), the Mean Value Theorem states that for an interval | 0, /], there is a point x = c in (0), / ) where the instantaneous rate of change at x = c is equal to the average rate of change between a and b. O For f(x) = sin(x), the Mean Value Theorem states that for an interval | 0, / |, there is a point x = c in ((), )where f(c) is equal to the average of f(b) and f(a). O For f(x) = sin(x), The Mean Value Theorem tells you how to find a value x = c in (a, b) such that the instantaneous rate of change at c is equal to the average rate of change between a and b. O For f(x) = sin(x), The Mean Value Theorem does not apply.Does the Mean Value Theorem apply to f ( x ) = between [-5, 5]? O f(x) is differentiable everywhere between (-5, 5) so MVT applies. O f(x) is differentiable and continuous everywhere in the interval between [-5, 5] so the MVT does apply. O f(x) is not differentiable everywhere in the interval between [-5, 5] so the MVT does not apply. O f(x) is not continuous between [-5, 5] so MVT applies.For f(x) = 3x2 + 1, find all the values of c on the interval (0, 2) that satisfy the Mean Value Theorem. O c= 1 O C= - 0.5 O C= 0 O C = 0.5For f(x) = cos(x), find all the values of c on the interval [0, /7 ] that satisfy the Mean Value Theorem. O c = 0.6901 and 2.4515 O C= 0 O CE - O c=-0.6901 and -2.4515If 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