Proof of inequality

[mta]

Hello,
I have the following question: if f is a convex function, we know that for every x, y and for every 0<=t<=1 we have f(tx+(1-t)y)<=tf(x)+(1-t)f(y), but how can we prove that f(tx+(1-t)y)>=tf(x)+(1-t)f(y) if t>=1.
Thanks

 

[Deleted member 4993]

Hello,
I have the following question: if f is a convex function, we know that for every x, y and for every 0<=t<=1 we have f(tx+(1-t)y)<=tf(x)+(1-t)f(y), but how can we prove that f(tx+(1-t)y)>=tf(x)+(1-t)f(y) if t>=1.
Thanks

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[Dr.Peterson]

Try sketching a graph of such a function, including the three points involved in the given inequality. Repeat for the required inequality. Can you find a way to relate the second drawing to the first (e.g. using different values of x and y)? Can you rewrite the required inequality to make it look more like the given inequality?

In any case, please obey the rules and show us something that you have thought about the problem, so we can have a place to start in helping you.