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Recall that a set is convex if and only if for all,. Suppose that is differentiable and that for some, for all. Which of the following is true?

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MCQs on Real Analysis.


Recall that a set<br><img src='https://www.fatskills.com/images2/GradExams/6835077B-6C02-4255-A0C8-A14103A687A4.png' height='15' width='64'/> is convex if and only if for all<br><img src='https://www.fatskills.com/images2/GradExams/74D79520-64A8-4AF8-BB0F-C777A99ACF5D.png' height='18' width='67'/>,<br><img src='https://www.fatskills.com/images2/GradExams/D8C40D30-DFB7-4823-B4F0-F0B88357E0AC.png' height='20' width='251'/>. Suppose that<br><img src='https://www.fatskills.com/images2/GradExams/547E4F67-E299-47A0-B4F7-A2CA35CEB4A9.png' height='19' width='143'/> is differentiable and that for some<br><img src='https://www.fatskills.com/images2/GradExams/3C66F696-7D66-4263-A94D-AB39BBB1E372.png' height='15' width='55'/>,<br><img src='https://www.fatskills.com/images2/GradExams/985B90EE-FC04-4944-9539-260F4AED39E9.png' height='20' width='96'/> for all<br><img src='https://www.fatskills.com/images2/GradExams/1273C686-B391-4D42-915A-60895C5D2EAB.png' height='16' width='49'/>. Which of the following is true?





 
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