Which of the following statements must be true? Select one: O a. If f'(4) = 0, the then f(x) has a local minimum at x = 4 O b. If f(x) has a local maximum at x = 5, then x = 5is a critical number of f(x) If f(x) has a local minimum at x = 2, then f'(2) = 0 O c. O d. If f(x) is continuous on the closed interval [1,4], then f(x) has a local minimum or a local maximum on [1,4]
Which of the following statements must be true? Select one: O a. If f'(4) = 0, the then f(x) has a local minimum at x = 4 O b. If f(x) has a local maximum at x = 5, then x = 5is a critical number of f(x) If f(x) has a local minimum at x = 2, then f'(2) = 0 O c. O d. If f(x) is continuous on the closed interval [1,4], then f(x) has a local minimum or a local maximum on [1,4]
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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![**Question:**
Which of the following statements must be true?
**Select one:**
- **a.** If \( f'(4) = 0 \), then \( f(x) \) has a local minimum at \( x = 4 \)
- **b.** If \( f(x) \) has a local maximum at \( x = 5 \), then \( x = 5 \) is a critical number of \( f(x) \)
- **c.** If \( f(x) \) has a local minimum at \( x = 2 \), then \( f'(2) = 0 \)
- **d.** If \( f(x) \) is continuous on the closed interval \([1,4]\), then \( f(x) \) has a local minimum or a local maximum on \([1,4]\)
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Transcribed Image Text:**Question:**
Which of the following statements must be true?
**Select one:**
- **a.** If \( f'(4) = 0 \), then \( f(x) \) has a local minimum at \( x = 4 \)
- **b.** If \( f(x) \) has a local maximum at \( x = 5 \), then \( x = 5 \) is a critical number of \( f(x) \)
- **c.** If \( f(x) \) has a local minimum at \( x = 2 \), then \( f'(2) = 0 \)
- **d.** If \( f(x) \) is continuous on the closed interval \([1,4]\), then \( f(x) \) has a local minimum or a local maximum on \([1,4]\)
**[Check Button]**
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