1. over what interval with the intermediate value theorem apply? a. {-5, -00001} b. (-5, -.00001) c. [-5,0] d. everywhere shown 2. The IVT is often used to verify that a function has a zero. For the following graph what would be the proper way to state the IVT theorem to show that there is a zero in the range? A. f(x) is continuous on [-6, -4] and let k be zero. Then there exists a number c such that, f(c) = 0. B. f(x) is continuous on [-5, 5] and let k be zero. Then there exists a number c such that, f(c) = 0 C. f(x) is continuous on [-2, 5] and let k be zero. Then there exists a number c such that, f(c) = 0. D. f(x) is continuous on [4, 5] and let k be zero. Then there exists a number c such that, f(c) = 0. 3. Imagine that you are driving along a turnpike, (toll road). At the beginning of the road you pickup a ticket and then after 10 miles you exit the road. The speed limit is 60 miles an hour and it only takes you 5 minutes to travel 10 miles. Can the police office at the end of the toll road prove (using the IVT) that you must have gone faster than 60 miles an hour at some point? A. no B. yes C. sometimes 4. Over what interval will the intermediate value theorem apply? a. [-2, 2.99999] b. [3.00001,8 ] c. both a and b d. everywhere 5. A diabetic measures her blood sugar in the morning and it is 150. Later in the day she measures it again and it is 100. Can she use the IVT to prove that at some point her blood sugar was 120? a. no b. yes c. some times 6. Use the IVT (Intermediate Value Theorem) to show that has a zero in the interval [-4,4]. A. f(x) is continuous on [-4,4], f(-4)= 13, f(4) = 13, so we can not use the IVT to show there is a zero. B. f(x) is continuous on [-4,4], f(-1)= -2, f(4) = 13, so we can use the IVT to show there is a zero, between [-1,4]. C. f(x) is continuous on [-4,4], f(-1)= -2, f(0) = -3, so we can use the IVT to show there is a zero, between [-1,0]. D. The IVT cannot be applied to find a zero. 7. Use the IVT (Intermediate Value Theorem) to show that has a zero. A. f(x) is continuous on [0,1], f(0) < 0 , f(1) = 0, so we can use the IVT to show there is a zero in [0,1] B. f(x) is continuous on [-1,2], f(-1) < 0 , f(2) > 0, so we can use the IVT to show there is a zero in [-1,2] C. f(x) is continuous on [-2,1], f(-2) < 0 , f(1) = 0, so we can use the IVT to show there is a zero, between [-2,1]. D. The IVT cannot be applied to find a zero. 8. If a swimmer dives into a pool, swims to the other side and then jumps out. Can you use the IVT (with the interval being at the start and finish) to show that the swimmer must have entered the water? A. No B. Yes 9. Use the IVT (Intermediate Value Theorem) to show that has a zero. A. f(x) is continuous on [-1,1], f(1)= -3, f(1) = -3, so we can use the IVT to show there is a zero in [-1,1] B. f(x) is continuous on [1,2], f(1)= -3, f(2) > 0, so we can use the IVT to show there is a zero in [1,2] C. f(x) is continuous on [-2,0], f(2) > 0 , f(0) = -3, so we can not use the IVT to show there is a zero, between [-2,0]. D. The IVT cannot be applied to find a zero