Liver Heaven (Liver Fiesta #5) Mystery Cache
Serrabou: This one started as a regular container near the trail—quite heavenly. But it’s a flood zone so it spent its final days 9’ up a tree. Buh-bye Liver 4.
Liver Heaven (Liver Fiesta #5)
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Difficulty:
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Terrain:
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Size: 
(micro)
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Welcome to Liver Heaven, the fifth Liver Cache in the Liver Fiesta Dodecathon!
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DO NOT GO TO THE POSTED COORDINATES! YOU MUST SOLVE THE PUZZLE BELOW TO GET THE CORRECT COORDINATES.
Liver Cachers! Here's a way to take advantage of what you've learned so far. If you've performed well to date, what follows will make sense and prepare you--to some extent--for the ultimate End of Liver cache. If not, you need to re-serve the liver in the Fiesta so far.
This Liver Cache contains a clue for the location of End of Liver.
(Confused? Visit the Cache Description for Liver Fiesta to obtain Liver Fiesta Dodecathon enlightenment.)
Liver Heaven is a typical cache that contains a log book, some trinkets, and, of course, a clue for the location of End of Liver .
Find the cache, get the clue, and move on to the next cache in the Liver Fiesta Dodecathon.
WAIT!
For Liver Heaven, the fifth Liver Fiesta Cache in the Liver Fiesta Dodecation, you need to solve the following problem to find the coordinates for the next clue. Then, and only then, can you find it, record it, and get ready for what comes next.
We know that the drivative of a function at a point is the slope of the tangent line at this point. The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency. Because the slopes of perpendicular lines (neither of which is vertical) are negative reciprocals of one another, the slope of the normal line to the graph of f(z) is -1/f'(z) or -1/(df/dz).
Find the equation of the normal line to the graph of
f(z) = (z2+3)½ = SQRT (z2+3)
at the point (-1,2).
Express your answer as a function of z, and then use that function to compute the corresponding digits of the coordinates for this heavenly Liver Fiesta cache.
The form of the function should be f(zi) = c1zi + c2, where c1 and c2 are constants.
The coordinates are:
N 38° f(z1)f(z2) . f(z3)f(z4)f(z5)
W 077° f(z6)f(z7) . f(z8)f(z9)f(z10)
...and the corresponding values for each zi are as follows:
z1 = T / 2
z2 = ( H - M ) / 2
z3 = M - R
z4 = ( R - M ) / 2
z5 = ( 3H - M - R ) / 2 (here "3H" means "3 times H")
z6 = ( 3T - H ) / 2
z7 = H - ( R + 3T ) / 2
z8 = R - H
z9 = ( H - T ) / 2
z10 = ( M - H ) / 2
Now, you may ask, why Liver Heaven? As all cachers know, traditional caches are rated according to difficulty of hide and difficulty of terrain. Puzzle caches have an added dimension of difficulty based on difficulty of puzzle. We can't comment on the difficulty of the puzzle for Liver Heaven; it depends on what you know. For the traditional aspects, however, Liver Heaven is "heavenly." Perhaps the next one will be more "hellish." That's Liver Caching for you...
Good luck, and Enjoy! 
BY THE WAY, PLEASE DO NOT POST A PICTURE OF THE CACHE CONTAINER IN YOUR LOG ENTRY. THANKS!!!
Additional Hints
(Decrypt)
[For Puzzle] Pnyphyhf bar-bu-bar naq cnl nggragvba gb gur frdhrapr bs qngrf uvqqra
[For Hide] Pnzb'rq fznyy cynfgvp wne unatvat