a. Determine whether the Mean Value Theorem applies to the function f(x) = 1-x on the interval [-2,1]. 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. No, because the function is differentiable on the interval (-2,1), but is not continuous on the interval [-2,1]. B. No, because the function is not continuous on the interval [-2,1], and is not differentiable on the interval (-2,1). C. No, because the function is continuous on the interval [-2,1], but is not differentiable on the interval (-2,1). O D. Yes, because the function is continuous on the interval [-2,1] and differentiable on the interval (- 2,1). 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.) B. The Mean Value Theorem does not apply in this case.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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a. Determine whether the Mean Value Theorem applies to the function f(x) = 1-x on the interval [-2,1].
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. No, because the function is differentiable on the interval (-2,1), but is not continuous on the interval [-2,1].
B. No, because the function is not continuous on the interval [-2,1], and is not differentiable on the interval (-2,1).
C. No, because the function is continuous on the interval [-2,1], but is not differentiable on the interval (-2,1).
O D. Yes, because the function is continuous on the interval [-2,1] and differentiable on the interval (- 2,1).
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.)
B. The Mean Value Theorem does not apply in this case.
Transcribed Image Text:a. Determine whether the Mean Value Theorem applies to the function f(x) = 1-x on the interval [-2,1]. 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. No, because the function is differentiable on the interval (-2,1), but is not continuous on the interval [-2,1]. B. No, because the function is not continuous on the interval [-2,1], and is not differentiable on the interval (-2,1). C. No, because the function is continuous on the interval [-2,1], but is not differentiable on the interval (-2,1). O D. Yes, because the function is continuous on the interval [-2,1] and differentiable on the interval (- 2,1). 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.) B. The Mean Value Theorem does not apply in this case.
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