11:35 myopenmath.com Question 7 0/6 pts 9 3 99 0 Details Consider the function f (ac) - 5ac3 - 4ac on the interval [-5, 5]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval (-5, 5) such that f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one is Question Help: Video Message instructor Submit Question Question 8 0/4 pts 9 3 99 0 Details myopenmath.com Question Help: El Video 8 Message instructor Submit Question 0 Question 11 B 0/5 pts '0 3 Z 99 CD Details If a rock is dropped from a height of 155 ft, its poistion t seconds after it is dropped until it hits the ground is given by the function 3(t) : 716t2 + 155. Round values below to 3 decimal places. How long does it take the rock to hit the ground? seconds Find the average velocity of the rock from when it is released until when it hits the ground. feet per second What time after the rock is thrown will its instantaneous velocity be equal to its average velcity? (Apply the Mean Value Theorem} seconds after it is thrOWn Question Help: 8 Message instructor Submit Question 0 Question 12 B 0/4 pom2M 11 :35 myopenmath.com Submit Question 0 Question 9 I24 0/6 pts '0 3 8 99 (D Details Consider the function f(:I:) = 6 sin() on the interval [0, 5]. 6J 1 2 3 Find the average or mean slope of the function on this interval. I l Enter at least 4 decimal places in your answer. By the Mean Value Theorem, we know there exists a c in the open interval (0, 5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. l J Enter at least 4 decimal places in your answer. Question Help: 8 Message instructor Submit Question myopenmath.com 0 Question 1 B 0/2 pts '0 3 8 99 G) Details Answer the following True or False: Let x) be a differentiable function, such that f(3) : 6 and f(1) : 10. Then there exists a c with 3 g c g 1 such that the tangent line to y 2 at) is horizontal at 33:6. Question Help: 8 Message instructor Submit Question 0 Question 2 a 0/2 pts '0 3 Z 99 (9 Details Answer the following True or False: Two cars drive from one spotlight to the next, leaving at the same time and arriving at the same time. Then there is a time when they are going the same speed. 11:35 myopenmath.com Question 4 0/5 pts ) 3 99 0 Details Question Details If we apply Rolle's Theorem cu Unit FunCLIVIl f(ae) = 2x2 - 16x - 3 on the interval [2, 6], how many values of c exist such that f'(c) = 0? What is the value of c? If we try to apply Rolle's Thorem to the function f (ac) = 2x2 - 16x - 3 on the interval [-1, 13], which of the following conditions is not met? O differentiability on (-1, 13) Of(a) = f(b) O continuty on [-1, 13] Question Help: Video Message instructor myopenmath.com ''""'l' " "'U instructor Submit Question 0 Question 8 B 0/4 pts '0 3 8 99 G Details Consider the function f(;L') = 4% + 8 on the interval [1, 7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1,7) such that f'((:) is equal to this mean slope. For this problem, there is only one c that works. Find it. Question Help: 8 Message instructor Submit Question 0 Question 9 B 0/6 pts '0 3 8 99 Details . a: Consider the function at) 2 651n() on 3 the interval [0, 5]. 6+ myopenmath.com 0 Question 5 E 0/5 pts '0 3 2 99 6) Details Consider the function f(a:) = :n2 10m + 4 on the interval [8, 2]. Evaluate this function at the endpoints of the interval. Does Rolle's Theorem apply to f on this interval? 0 Yes 0 No If Rolle's Theorem applies, find 6 in (8, 2) such that f' (c) = 0. If Rolle's Theorem does not apply, enter "DNE". c=_ Question Help: 8 Message instructor Submit Question 11:36 myopenmath.com Submit Question Question 10 0/5 pts 9 3 99 0 Details Consider the function f(x) = 1 22 on the interval [-1, 1]. a. Is f(-1) = f(1)? Yes No OO b. Is f continuous on [-1, 1]? Yes No c. Is f differentiable on (-1, 1)? Yes No OO d. What do your answers to parts a. , b., and c. imply? O Rolle's Theorem can be applied O The Mean Value Theorem can be applied O Both Rolle's Theorem and the Mena Value Theorem can be applied ONeither Rolle's Theorem nor the Mean Value Theorem applies to this problem e. If you can use Rolle's Theorem or the Mean Value Theorem, find the value of c satisfying said theorem. If not, enter DNE. Answers should be in exact form (i.e., do not use a calculator to get a decimal approximation). C = Bug Bounty Question Help: Video Message instructor Submit Question Question 11 0/5 pts 9 3 99 0 Details myopenmath.com Submit Question 0 Question 6 B 0/4 pts '0 3 Q 99 G) Details Consider the function f(:c) : 3 53:2 on the interval [3, 3]. Find the average or mean slope of the function on this interval, i.e. f (3) f (3) _ 3 (3) _ By the Mean Value Theorem, we know there exists a c in the open interval (3, 3) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Question Help: S Video 8 Message instructor Submit Question 0 Question 7 B 0/6 pts '0 3 Z 99 (9 Details Consider the function f(w) : 5:133 43: on the interval [Mraqe or myopenmath.com 0 Question 12 B 0/4 pts '0 3 Z 99 6) Details At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second police car at 55mph at 10:53 a.m., which is located 39 miles from the first police car. If the speed limit is 70mph, can the police cite you for speeding? Find your average velocity from the 10:17 am. to 10:53 am. Round value above to 2 decimal places. By the MVT, since the average velocity over the interval was Select an answer 0 than the posted speed limit of 70mph the police Select an answer 0 site you for speeding. Question Help: 8 Message instructor Submit