Prove or disprove If |f(x)-f(t)| <=(x-t)^2 for all x, t E R, then f is uniformly

Question

Prove or disprove If |f(x)-f(t)| <=(x-t)^2 for all x, t E R, then f is uniformly continuous on R. I am not sure how to form the difference quotient form of the equation. and well I know to show f is uniformly continuous you have to show on a domain that it is uniformly continuous. and well I believe that f must be a constant function if |f(x)-f(t)|<=(x-t)^2 and to prove all this the sandwich theorem can be used. I think the biggest issue I am having is transforming the equation into a difference quotient

Explanation / Answer

check it http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDkQFjAB&url=http%3A%2F%2Fwww.math.ttu.edu%2F~lhoang%2FM4606-Fall06%2Fchapter6%2B7.pdf&ei=fYe-UN6qJNHciQLPiYGgAw&usg=AFQjCNFH9llB6NIe3pDlJq62n1mKvgJVgA&sig2=qdm31NY3EXbiXq3rUPTY2Q

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