Dr. Stevens, for the derivative to solve for critical thickness, the symbolic equals should use the key word solve,t since we are solving for t (thickness). Answer is k/h-R as expected. A note should be added that the the critical thickness is ONLY dependent on the the coefficients as R is the radius of the pipe 
. Working on a comprable sheet, which is why I requested help. Your sheet "solved" my conundrum ... I was using the programming add bar instead of stacking the symbolic keywords. Many thanks
