If f(x) = tan(x), does the Mean Value Theorem apply on the interval [0, 7] and why? O The Mean Value Theorem applies because, f(@) is differentiable on the closed interval [0, 7]. O The Mean Value Theorem applies because f (@ ) is differentiable on the open interval (0, ). The Mean Value Theorem does not apply because f(@) is not continuous on the closed interval [0, 7]. O The Mean Value Theorem applies because f(@) is continuous on [0, 7].Does the Mean Value Theorem apply to f (ac ) = between [1, 5]? O f(x) is continuous between [1, 5] so MVT applies. O f(x) is differentiable everywhere in the interval between [1, 5] so the MVT does apply. O f(x) is neither differentiable nor continuous everywhere in the interval between [1, 5] so the MVT does not apply. O f(x) is not differentiable everywhere between [1, 5] so MVT does not apply.For f(x) = 3x2 + 1, find all the values of c on the interval (0, 2) that satisfy the Mean Value Theorem. O c= - 0.5 O C= 0 O c= 1 O c = 0.5For f(x) = sin(x), nd all the values of c on the interval [0, 1r ) that satisfy the Mean Value Theorem. 0 c=% O c=1 O c=% Let f(x) = x2 3x. Use Rolle's Theorem to find all the values of x = c in the interval [0, 3] such that f '(c} = 0. O c=1.5 O c=1 O c=3 Let x) = sin(x). Use Rolle's Theorem to find all the values of x = c in the interval [0, 7r ] such that f '(c) = O. O c=1 O c=% 0 0:0 Which of the following is true? 0 If Rolle's Theorem can be applied it is possible that the Mean Value Theorem cannot be applied. 0 Rolle's Theorem is a special case of the Mean Value Theorem. 0 The Mean Value Theorem is a special case of Rolle's Theorem. 0 If the Mean Value Theorem is applied then Rolle's Theorem is automatically applicable. For the function f(x) = sin(x), on the interval [0, 7r ], which of the following is true? For f(x) = sin(x), The Mean Value Theorem tells you how to nd a value x = c in (a, b) such that the instantaneous rate of 0 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 states that for an interval [0, 7r], there is a point x = c in (U, 7r)where f(c) is equal to the average of f(b) and f(a). O For f(x) = sin(x), the Mean Value Theorem states that for an interval [0, 7r], there is a point x = c in (0, 7r) 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 does not apply. 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 12 miles later at 12:10. Using the Mean Value Theorem, can you prove that Bob was driving faster than 55 miles per hour at some point? Bob's average speed was 72 milesi'hr and the Mean Value Theorem cannot be used to prove that he was traveling faster 0 than 55 miles per hour at some point between the two toll readers. Bob's average speed was 60 milesfhr 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. Bob's average speed was 60 milesi'hr and the Mean Value Theorem can be used to prove that he was traveling fasterthan 55 miles per hour at some point between the two toll readers. Bob's average speed was 72 milesfhr 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. Sue is a diabetic and tests her blood sugar levels often. When she woke up Monday morning at 7:00, her blood sugar was 100 mg. After breakfast at 9:00 her blood sugar was too high - 200 mg - so she took insulin. At 11 :00 her blood sugar was 120 mg, which is the normal range. Which of the following is true? The Mean Value Theorem applies, as blood sugar levels can be assumed to be continuous and differentiable. The O . _ . average rate of change is: f(9.00} 2 lm) 2 T1200 2 50 mg / hr 0 Blood sugar levels cannot be assumed to be differentiable so the Mean Value Theorem will not hold. 0 Blood sugar levels cannot be assumed to be continuous so the Mean Value Theorem will not hold. The Mean Value Theorem applies as blood sugar levels can be assumed to be continuous and differentiable. The average 0 . _ . rate of change is: w = g = 50 mgr/hr