can anyone tell me what a negative value of the critical radius of insulation would tell me?

from differentiation is giving as

x = klag/hout

where x = radius of lagged pipe, k is the thermal conductivity of the lagging material and h is the heat loss out side of the lagging.

an explanation is that if the critical radius is less than the radius of the unlagged pipe then the heat transfer would decrease with any increase in lagging - with a minimum at the critical density.

if the radius of the unlagged pipe is less than the critical density the opposite is true