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7. Let f : [0, 1] →R be a convex function with f(0) = 0. Which of the following is always true for f? A. f is differentiable B. f may not be differentiable but it is continuous C. f(x) 2 xf'(x) for all æ E [0, 1] if ƒ is differentiable D. попe of the above

7. Let f : [0, 1] →R be a convex function with f(0) = 0. Which of the following is always true for f? A. f is differentiable B. f may not be differentiable but it is continuous C. f(x) 2 xf'(x) for all æ E [0, 1] if ƒ is differentiable D. попe of the above

Advanced Engineering Mathematics
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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Please answer the question given in the image with a proof. Is D really the correct answer?

Please provide a proof. 

7. Let f : [0, 1] → R be a convex function with f(0) = 0. Which of the following is always true for f? A. f is differentiable B. f may not be differentiable but it is continuous C. f(x) > xf'(x) for all a E [0, 1] if ƒ is differentiable D. none of the above
Transcribed Image Text:7. Let f : [0, 1] → R be a convex function with f(0) = 0. Which of the following is always true for f? A. f is differentiable B. f may not be differentiable but it is continuous C. f(x) > xf'(x) for all a E [0, 1] if ƒ is differentiable D. none of the above
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