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Can the word "sufficient" be used in a negative sense, i.e. relating to something that has a negative effect when augmented? Example:

These problems influence the results for sufficiently high speeds.

Since "sufficient" is a fundamental logical concept (as the logical opposite of "necessary"), I feel it shouldn't be "biased" in this way. On the other hand, maybe in linguistics it is different. The meaning of "sufficient" is equivalent to "as much as needed", so I can imagine that the "positive" nature of the verb "need" influences the meaning here.

So, can "sufficient/ly" be used in this way?

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I see nothing wrong with that sentence. Here's one of my favorites you see on the internet that uses "sufficiently" in a similar manner (sometimes known as Grey's Law):

Sufficently advanced incompetence is indistinguishable from malice.

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    King James bible too: Sufficient unto the day is the evil thereof. bible.cc/matthew/6-34.htm
    – Wayfaring Stranger
    Apr 10, 2012 at 13:59
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    I do love me some KJV. However, its language is rather archaic, so its probably not the best supporting reference for modern English.
    – T.E.D.
    Apr 10, 2012 at 15:33
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Short answer: Yes.

"Sufficient" in this context means "enough to produce the specified result." Whether that result is desirable or not is irrelevant. Indeed, in some cases it could depend on point of view. Like, "XYZ Company had sufficient influence with the administration to push through a multi-million dollar government bailout." The result is positive from XYZ's point of view, not so positive from the taxpayers'.

I understand your problem. Some words imply a positive connotation. Like I recall when a news organization here in the U.S. announced a new policy that they would no longer say, "[whoever] claimed credit for the terrorist attack yesterday", but rather, "[whoever] claimed RESPONSIBILITY for the terrorist attack", on the reasoning that the word "credit" implies something positive. Of course the people launching such an attack presumably do see it as a positive accomplishment, so they are claiming "credit".

BTW, I'd say the logical opposite of "sufficient" is "insufficient". "Necessary" isn't really the opposite of "sufficient", but rather a different degree of the quantity under consideration. (Usually using "quantity" here in a metaphorical sense, like "Divisibility by 2 is a necessary but not a sufficient condition ...")

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