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MTH424 Convex Analysis
Instructions: (one must follow the instructions)
• You may submit the assignment in group.
• Please make sure that the PDF or other file is good before sending.
• Please send email only once.
• Do not forget to read the academic honesty requirement before sending.
Question # 1
Prove that if is convex on I, then f(x)=(f(x)-f(c))/(x-c), x≠c is increasing on I.
Question # 2
If f is convex on[a,b], then prove that f((a+b)/2)≤(f(a)+f(b))/2.
Academic Honesty Requirements:
You are encouraged to work with others in the completion of assignments, but it doesn’t include copying. However, in the spirit of Academic Honesty, which includes crediting others for their contribution to your work, please include one of the following statements with every submitted assignment on title page:
1. I worked alone on this assignment and write myself.
2. I worked with the following: List their full names. Include their relationship to you if they are not also a member of this class and write myself.