QUESTION 3 Consider the following statements: (i) If f: [a,b] → R is differentiable on (a,b) and f(a) = f(b), then f'(c) = 0 for some c = (a,b). (ii) If f: [a,b]→R satisfies f'(c)=0 for all c = (a,b), then f is constant. Which statements are true? Statement (ii), but not statement (i), is true. O Neither statement is true. Both statements are true. O Statement (i), but not statement (ii), is true.
QUESTION 3 Consider the following statements: (i) If f: [a,b] → R is differentiable on (a,b) and f(a) = f(b), then f'(c) = 0 for some c = (a,b). (ii) If f: [a,b]→R satisfies f'(c)=0 for all c = (a,b), then f is constant. Which statements are true? Statement (ii), but not statement (i), is true. O Neither statement is true. Both statements are true. O Statement (i), but not statement (ii), is true.
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 3
Consider the following statements:
(i) If f: [a,b] → R is differentiable on (a,b) and f(a) = f(b), then f'(c) = 0 for some c = (a,b).
(ii) If f: [a,b]→R satisfies f'(c)=0 for all c = (a,b), then f is constant.
Which statements are true?
Statement (ii), but not statement (i), is true.
O Neither statement is true.
Both statements are true.
O Statement (i), but not statement (ii), is true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd22a7882-835a-44a8-b8af-d7a415b67cf6%2F88fb96d5-644c-4936-a58b-02737e32063b%2Fselvg2q_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 3
Consider the following statements:
(i) If f: [a,b] → R is differentiable on (a,b) and f(a) = f(b), then f'(c) = 0 for some c = (a,b).
(ii) If f: [a,b]→R satisfies f'(c)=0 for all c = (a,b), then f is constant.
Which statements are true?
Statement (ii), but not statement (i), is true.
O Neither statement is true.
Both statements are true.
O Statement (i), but not statement (ii), is true.
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