With
p[x_, left_, right_] := UnitStep[x - left] UnitStep[right - x]
f1 = (1400 + 200 #) p[#, 0, 0.77] &;
f2 = 3460 # p[#, 0, 0.36] &;
f3 = (1172 + 214 #) p[#, 0.36, 0.77] &;
How about
Plot[{f1@x, If[f2@x >= f3@x, f2@x, f3@x]}, {x, 0, 0.77}, Filling -> {1 -> {2}}]

Or
Plot[{f1@x, If[f2@x >= f3@x, f2@x, f3@x], f2@x, f3@x}, {x, 0, 0.77}, Filling -> {1 -> {2}}, Exclusions -> All]

It's better to use UnitStep
instead of HeavisideTheta
, becasue with the former one gets a simple derivative (and the discountinuity can be easily located):

while one get a messy output for the latter:

FunctionDomain[the f functions, t]
also don't work with HeavisideTheta
, but yield True
for the UnitStep
case.