Question

7. a. Determine whether the Mean Value Theorem applies to the function f(x) = 7 - x? on the interval (-1,2) b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. a. Choose the correct answer below. O A. Yes, because the function is continuous on the interval [-1.2] and differentiable on the interval (-1.2). O B. No, because the function is differentiable on the interval (-1.2), but is not continuous on the interval (-1,2]. OC. No, because the function is not continuous on the interval (-1,2), and is not differentiable on the interval (-1,2). OD. No, because the function is continuous on the interval [-1,2], but is not differentiable on the interval (-1,2). b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The point(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) OB. The Mean Value Theorem does not apply in this case. 8. A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 28 mi along the highway. When the car reached the location of the second officer 22 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60 mihr speed limit. Why can the officer conclude that the driver exceeded the speed limit? Select the correct answer below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to the nearest hundredth as needed.) O A. The officer can conclude the driver exceeded the speed limit because, by the Mean Value Theorem, at some time, miles per hour. O B. The officer can conclude the driver exceeded the speed limit because, by Rolle's Theorem, at some time c, the car w miles per hour. O C. The officer can conclude the driver exceeded the speed limit because, by the Extreme Value Theorem, at some time miles per hour. 9. Find the intervals on which is increasing and the intervals on which it is decreasing f(x)=x? Inx? +3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on and increasing on (Simplify your answers. Use a comma to separate answers as needed. Type your answers in interval notation. Type: exact answers, using radicals as needed.) O B . The function is decreasing on The function is never increasing (Simplify your answer. Use a comma to separate answers as needed. Type your answer in interval notation. Type an an exact answer, using radicals as needed.) O C. The function is increasing on The function is never decreasing (Simplify your answer. Use a comma to separate answers as needed. Type your answer in interval notation. Type an an exact answer, using radicals as needed.) OD. The function is never increasing or decreasing

Answer 1

Given fon) = qr? [-1, 2] Since fino es a folynomial therefore it is continuous in [1, 2] & differentiable in (-1,2). Hence Mean value theorem can be applied obtion ② is correct f(x)= -20 fle)= -20 f(2)= 7(2)?= 7-4-3 f67)=7-45= 11=6 Applying M. V.T. f(c) = f(b)-fla) = f(2lfG) bra -20 = 356 = zaled seat € 1,23 2 + ca Stance 6 point is (1 = 1/2)