5. Let f : [0, 1] → R be twice differentiable. Suppose that the line segment joining the points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a < 1. Then, A. there exists z E [0, 1] such that f'(z) = 0 B. there exists z E [0, 1] such that f"(2) = |f(1) – f(0)| C. there exists z e [0, 1] such that f"(2) = f(1) – f(0) D there exists zE [0 11 such that f"(-) = 0
5. Let f : [0, 1] → R be twice differentiable. Suppose that the line segment joining the points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a < 1. Then, A. there exists z E [0, 1] such that f'(z) = 0 B. there exists z E [0, 1] such that f"(2) = |f(1) – f(0)| C. there exists z e [0, 1] such that f"(2) = f(1) – f(0) D there exists zE [0 11 such that f"(-) = 0
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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The question is attached in the image. Please provide a proof for the correct asnwer. If possible, please rule out the incorrect options as well. Thank you.
![5. Let f : [0, 1] → R be twice differentiable. Suppose that the line segment joining the
points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a <
1. Then,
A. there exists z E [0, 1] such that f'(2) = 0
B. there exists z e [0, 1] such that f"(2) = |f(1) – f(0)|
C. there exists z e [0, 1] such that f"(z) = f (1) – f(0)
D. there exists z E [0, 1] such that f"(z) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f4412a-18c0-4f64-8bcf-4dffb42656da%2F1cd54a51-e96e-43a4-a665-9ebee4440bbd%2Fao11bcd_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let f : [0, 1] → R be twice differentiable. Suppose that the line segment joining the
points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a <
1. Then,
A. there exists z E [0, 1] such that f'(2) = 0
B. there exists z e [0, 1] such that f"(2) = |f(1) – f(0)|
C. there exists z e [0, 1] such that f"(z) = f (1) – f(0)
D. there exists z E [0, 1] such that f"(z) = 0
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