The Missing Link Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(small)
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Thanks to Hikerjamz for letting me adopt this one!!
DO NOT GO TO THE ABOVE COORDINATES!! The cache coordinates listed are not correct, however the real coordinates are within city limits. I got this idea from a cacher down in Dayton; props to gallaghd. Now, I could have plagiarized his cache description, but have decided not to. For this puzzle cache, I have left a out a digit in the coords given below ("X") and it is up to you to figure out what it is. There are several plausible locations, but one will find you the smiley. Good Luck. You can find the cache at N40 08.300 084 14.X79 If you don't want to try this plug & chug method, the given mathematical hint will give you the number you need. Hint to find the digit: Does the curve y = (x^4 - 2x^2 + 2) have any horizontal tangents, if so, where? Your answer is the missing digit. All numbers for this problem are positive & greater than zero. [Remember you'll find the "horizontal" tangent when the curve reaches the apropriate positive or negative peak of the slope.]
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Additional Hints
(Decrypt)
Uvag gb svaq gur pnpur: Ornpu Oblf fbat (svyy va gur oynaxf) "N __ __ Oybaqr Unveqb, Fhesva HFN"