edits; simplify caching

CwJ/derivatives/related_rates.jmd

@@ -224,7 +224,7 @@ Solving, yields:
 ```
 
 
-* If $l = 12$ and $db/dt = 2$ when $b=4$, find $dh/dt$.
+* If when $l = 12$ it is known that $db/dt = 2$ when $b=4$, find $dh/dt$.
 
 We just need to find $h$ for this value of $b$, as the other two quantities in the last equation are known.
 
@@ -242,6 +242,9 @@ height = sqrt(length^2 - bottom^2)
 As $b$ goes to $l$, $h$ goes to ``0``, so $b/h$ blows up. Unless $db/dt$
 goes to $0$, the expression will become $-\infty$.
 
+!!! note
+    Often, this problem is presented with ``db/dt`` having a constant rate. In this case, the ladder problem defies physics, as ``dh/dt`` eventually is faster than the speed of light as ``h \rightarrow 0+``. In practice, were ``db/dt`` kept at a constant, the ladder would necessarily come away from the wall. The trajectory would follow that of a tractrix were there no gravity to account for.
+
 
 ##### Example