True or false

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  • #1
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Homework Statement



1. if a function is twice continuously differentiable with f''(x) >= 0 for all real values of x then

(f(-x) + f(x))/2 >= f(0) ?


2. if a function is twice continuously differentiable with f''(x) >= 0 for all real values of x then
tf(x) + (1-t)f(y) >= f(tx+(1-t)y)
for all real values of x and y and for 0<=t<=1


I am really confused with these types of questions and to how to attempt them in my exam.

Thanks
 

Answers and Replies

  • #2
jbunniii
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If [itex]f''(x) \geq 0[/itex] for all real x, then what kind of function is f?
 
  • #3
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convex?
 
  • #5
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No idea?
 
  • #7
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when i try and look it up it just keeps telling me exactly what part 2 says, i know its true but i need to prove it you see.
 
  • #8
jbunniii
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Yes, the conclusion of part 2 is exactly the definition of a convex function.

So part 2 is asking, true or false, f''(x) >= 0 for all x implies that f is convex. This is true, and the proof is a standard one which should be in your calculus book under "second derivative test" or something similar.

What about part 1?
 

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