Here is a old post regarding this questions below
(http://www.mathematicsgre.com/viewtopic ... 8+64#p1799)
Ques: Suppose that f is a continuous realvalued function defined on the closed interval [0,1]. Which of the following must be true ?
III. There is a constant E > 0 such that f(x) f(y) <= E xy for all x and y in [0,1]
The answer rejected III. The discussion said that not all the function are uniformly continuous.
But if we rewrite the condition as:
f(x) f(y) / xy = K <= E
So the left hand side become the abs of the slope. I am wondering for a continuous function defined on a closed interval, is it possible that the slope in not bounded?
GR9768 Q 64 Option 3? slope bounded?

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 Joined: Sun Apr 04, 2010 1:08 pm
Re: GR9768 Q 64 Option 3? slope bounded?
Any nonLipschitz function does the job
consider the square root of x...
consider the square root of x...
Re: GR9768 Q 64 Option 3? slope bounded?
That's a brilliant example. Thank youblitzer6266 wrote:Any nonLipschitz function does the job
consider the square root of x...