Problem #1: Suppose that f(4)=6 and f(9)=7. Which of the following statements must be true?(i) If f(x) is continuous on [4, 9] and differentiable on (4, 9) then there is a number c in (4, 9) such thatƒ'(c) = 1.(ii) If f(x) is continuous on [4, 9] and differentiable on (4, 9) then there is a number c in (4, 9) such thatf'(c) = 0.(iii) fis differentiable on (4,9).(A) (i) only (B) (i) and (iii) only (C) (ii) only (D) (i) and (ii) only (E) none of them (F) (iii) only(G) all of them (H) (ii) and (iii) only

Answered: Image /qna-images/answer/4dde75e6-4f4d-4caa-b260-7fb9b9ba3499.jpg

Suppose that f(4) = 6 and f(9) = 7. Which of the following statements must be true? (i) If f(x) is continuous on [4, 9] and differentiable on (4, 9) then there is a number c in (4, 9) such that f'(c) 3. (ii) If f(x) is continuous on [4, 9] and differentiable on (4,9) then there is a number c in (4,9) such that f'(c) = 0. (iii) f is differentiable on (4,9). (A) (i) only (B) (i) and (iii) only (C) (ii) only (D) (i) and (ii) only (E) none of them (F) (iii) only (G) all of them (H) (ii) and (iii) only

Suppose that f(4) = 6 and f(9) = 7. Which of the following statements must be true? (i) If f(x) is continuous on [4, 9] and differentiable on (4, 9) then there is a number c in (4, 9) such that f'(c) 3. (ii) If f(x) is continuous on [4, 9] and differentiable on (4,9) then there is a number c in (4,9) such that f'(c) = 0. (iii) f is differentiable on (4,9). (A) (i) only (B) (i) and (iii) only (C) (ii) only (D) (i) and (ii) only (E) none of them (F) (iii) only (G) all of them (H) (ii) and (iii) only

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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