1. If f : [a, b] → R and f(a)f(b) < 0, then f has a root in [a, b]. 2. Every subset of R which is bounded has an infimum. 3. Bracketing methods are assured to converge as long as the conditions of the IVT are satisfied.

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. STATE WHETHER THE FOLLOWING STATEMENT Is TRUE OR FALSE
1. If f : [a, b] → R and f(a)f(b) < 0, then f has a root in [a, b].
2. Every subset of R which is bounded has an infimum.
3. Bracketing methods are assured to converge as long as the conditions of the IVT are satisfied.
4. Open methods always converge.
5. The Extreme Value Theorem states that if f : [a, b] –→ R is continuous, then f attains a maximum
and a minimum on [a, b). By the Rolle's Theorem, it follows that the maximum and minimum are
critical points.
Transcribed Image Text:A. STATE WHETHER THE FOLLOWING STATEMENT Is TRUE OR FALSE 1. If f : [a, b] → R and f(a)f(b) < 0, then f has a root in [a, b]. 2. Every subset of R which is bounded has an infimum. 3. Bracketing methods are assured to converge as long as the conditions of the IVT are satisfied. 4. Open methods always converge. 5. The Extreme Value Theorem states that if f : [a, b] –→ R is continuous, then f attains a maximum and a minimum on [a, b). By the Rolle's Theorem, it follows that the maximum and minimum are critical points.
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