Let f be a function defined on [0,1]. Which of the choices is not enough to prove "f(x) >0 for all x on [0,1] is false"? (A) For all x, f(x) <0; (B) There is an x in [0,1] satisfying f(x) <0; (C) There is one x in [0,1] satisfying f(x)=0; (D) f(x) is nonnegative for all x.
Let f be a function defined on [0,1]. Which of the choices is not enough to prove "f(x) >0 for all x on [0,1] is false"? (A) For all x, f(x) <0; (B) There is an x in [0,1] satisfying f(x) <0; (C) There is one x in [0,1] satisfying f(x)=0; (D) f(x) is nonnegative for all x.
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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![**Question:**
Let \( f \) be a function defined on \([0,1]\). Which of the choices is not enough to prove "f(x) > 0 for all x on [0,1] is false"?
**Choices:**
(A) For all \( x \), \( f(x) < 0 \);
(B) There is an \( x \) in \([0,1]\) satisfying \( f(x) < 0 \);
(C) There is one \( x \) in \([0,1]\) satisfying \( f(x) = 0 \);
(D) \( f(x) \) is nonnegative for all \( x \).
- O A
- O B
- O C
- O D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd76a2d57-02e6-4734-ba8a-6fadc8c476a5%2Fd6c2e062-9462-4411-b5da-d8049ecfe73f%2Fb595jgw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Let \( f \) be a function defined on \([0,1]\). Which of the choices is not enough to prove "f(x) > 0 for all x on [0,1] is false"?
**Choices:**
(A) For all \( x \), \( f(x) < 0 \);
(B) There is an \( x \) in \([0,1]\) satisfying \( f(x) < 0 \);
(C) There is one \( x \) in \([0,1]\) satisfying \( f(x) = 0 \);
(D) \( f(x) \) is nonnegative for all \( x \).
- O A
- O B
- O C
- O D
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