Consider the following function and closed interval. Ах) - х3 - 3х + з, [-2, 2] Is f continuous on the closed interval [-2, 2]? O Yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem. O Yes, fis continuous on [-2, 2] and differentiable on (-2, 2) since polynomials are continuous and differentiable on R. O No, fis not continuous on [-2, 2]. O No, fis continuous on [-2, 2] but not differentiable on (-2, 2). O There is not enough information to verify if this function satisfies the mean value theorem. If fis differentiable on the open interval (-2, 2), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(-2) and f(2). (If an answer does not exist, enter DNE.) f(-2) = f(2) = Find Kb) - Ra) for [a, b) = (-2, 21. (If an answer does not exist, enter DNE.) b- a f(b) - f(a) b-a Determine whether the mean value theorem can be applied to f on the closed interval [-2, 2]. (Select all that apply.) O Yes, the Mean Value Theorem can be applied. O No, because fis not continuous on the closed interval [-2, 2]. O No, because fis not differentiable on the open interval (-2, 2). f(b) - f(a) b - a O No, because is not defined. If the mean value theorem can be applied, find all values of c that satisfy the conclusion of the mean value theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
Consider the following function and closed interval. Ах) - х3 - 3х + з, [-2, 2] Is f continuous on the closed interval [-2, 2]? O Yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem. O Yes, fis continuous on [-2, 2] and differentiable on (-2, 2) since polynomials are continuous and differentiable on R. O No, fis not continuous on [-2, 2]. O No, fis continuous on [-2, 2] but not differentiable on (-2, 2). O There is not enough information to verify if this function satisfies the mean value theorem. If fis differentiable on the open interval (-2, 2), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(-2) and f(2). (If an answer does not exist, enter DNE.) f(-2) = f(2) = Find Kb) - Ra) for [a, b) = (-2, 21. (If an answer does not exist, enter DNE.) b- a f(b) - f(a) b-a Determine whether the mean value theorem can be applied to f on the closed interval [-2, 2]. (Select all that apply.) O Yes, the Mean Value Theorem can be applied. O No, because fis not continuous on the closed interval [-2, 2]. O No, because fis not differentiable on the open interval (-2, 2). f(b) - f(a) b - a O No, because is not defined. If the mean value theorem can be applied, find all values of c that satisfy the conclusion of the mean value theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
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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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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