Answered: 1. If f : [a, b] → R and f(a)f(b) < 0,… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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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.

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