Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 7x³, [1, 2] Yes, the Mean Value Theorem can be applied. No, because fis not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = f(b) f(a), (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) b-a c =

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Determine whether the Mean Value Theorem can be applied to \( f \) on the closed interval \([a, b]\). (Select all that apply.)**

\[ f(x) = 7x^3, \quad [1, 2] \]

- [ ] Yes, the Mean Value Theorem can be applied.
- [ ] No, because \( f \) is not continuous on the closed interval \([a, b]\).
- [ ] No, because \( f \) is not differentiable in the open interval \((a, b)\).
- [ ] None of the above.

**If the Mean Value Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that**

\[ f'(c) = \frac{f(b) - f(a)}{b - a} \]

(Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.)

\[ c = \boxed{} \]
Transcribed Image Text:**Determine whether the Mean Value Theorem can be applied to \( f \) on the closed interval \([a, b]\). (Select all that apply.)** \[ f(x) = 7x^3, \quad [1, 2] \] - [ ] Yes, the Mean Value Theorem can be applied. - [ ] No, because \( f \) is not continuous on the closed interval \([a, b]\). - [ ] No, because \( f \) is not differentiable in the open interval \((a, b)\). - [ ] None of the above. **If the Mean Value Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that** \[ f'(c) = \frac{f(b) - f(a)}{b - a} \] (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) \[ c = \boxed{} \]
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