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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
icon
Related questions
Question
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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage