Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = -x² + 7x, [0, 7]

Calculus: Early Transcendentals
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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 Rolle's Theorem can be applied to \( f \) on the closed interval \([a, b]\).
(Select all that apply.)

\[ f(x) = -x^2 + 7x, \quad [0, 7] \]

- [x] Yes, Rolle's 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 \((a, b)\).
- [ ] No, because \( f(a) \ne f(b)\).

### If Rolle's Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that \( f'(c) = 0 \).
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

\( c = \) [_________]
Transcribed Image Text:### Determine whether Rolle's Theorem can be applied to \( f \) on the closed interval \([a, b]\). (Select all that apply.) \[ f(x) = -x^2 + 7x, \quad [0, 7] \] - [x] Yes, Rolle's 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 \((a, b)\). - [ ] No, because \( f(a) \ne f(b)\). ### If Rolle's Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that \( f'(c) = 0 \). (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) \( c = \) [_________]
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