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if f- is continuous on [4₁3] what must be true using IVT: A. there is some x on [4,0] where f(x) = Ø B. there is some x on [-1,0] where f(x) = 4 Co there is some x on [-1,3] where f(x) = 4 - X f(x) -4-6 -13 0 1 310

if f- is continuous on [4₁3] what must be true using IVT: A. there is some x on [4,0] where f(x) = Ø B. there is some x on [-1,0] where f(x) = 4 Co there is some x on [-1,3] where f(x) = 4 - X f(x) -4-6 -13 0 1 310

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Transcription: Continuity and the Intermediate Value Theorem** If \( f \) is continuous on the interval \([-4, 3]\), what must be true using the Intermediate Value Theorem (IVT)? - **A:** There is some \( x \) on \([-4, 0]\) where \( f(x) = \varnothing \). - **B:** There is some \( x \) on \([-1, 0]\) where \( f(x) = 4 \). - **C:** There is some \( x \) on \([-1, 3]\) where \( f(x) = 4 \). **Table** The table provides values for \( x \) and their corresponding function values \( f(x) \): \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -6 \\ -1 & 3 \\ 0 & 1 \\ 3 & 10 \\ \hline \end{array} \] **Explanation:** The Intermediate Value Theorem (IVT) states that if a function \( f \) is continuous on a closed interval \([a, b]\), and \( N \) is any number between \( f(a) \) and \( f(b) \), then there is at least one number \( c \) in the interval \([a, b]\) such that \( f(c) = N \). Given that the function \( f \) is continuous on \([-4, 3]\), we must determine which of the statements (A, B, or C) can be inferred as true based on the IVT and provided information.
Transcribed Image Text:**Transcription: Continuity and the Intermediate Value Theorem** If \( f \) is continuous on the interval \([-4, 3]\), what must be true using the Intermediate Value Theorem (IVT)? - **A:** There is some \( x \) on \([-4, 0]\) where \( f(x) = \varnothing \). - **B:** There is some \( x \) on \([-1, 0]\) where \( f(x) = 4 \). - **C:** There is some \( x \) on \([-1, 3]\) where \( f(x) = 4 \). **Table** The table provides values for \( x \) and their corresponding function values \( f(x) \): \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -6 \\ -1 & 3 \\ 0 & 1 \\ 3 & 10 \\ \hline \end{array} \] **Explanation:** The Intermediate Value Theorem (IVT) states that if a function \( f \) is continuous on a closed interval \([a, b]\), and \( N \) is any number between \( f(a) \) and \( f(b) \), then there is at least one number \( c \) in the interval \([a, b]\) such that \( f(c) = N \). Given that the function \( f \) is continuous on \([-4, 3]\), we must determine which of the statements (A, B, or C) can be inferred as true based on the IVT and provided information.
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f is continuous on open square brackets negative 4 comma space 3 close square brackets

x
f open parentheses x close parentheses
negative 4
negative 6
negative 1
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3
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