hello all
i'm trying to prove that the following function
f(v,e) = -9v^4 +26v^3 - 2v^2 - 83v -20 + 36ev^2 - 92ev - 36e^2 + 132

is negative when v>=5 and e>=2 , e<= 0.5*(v-1)*(v-2).
how do i do this? do i just substitute the the boundaries of e
(i.e. e=2 , e = 0.5*(v-1)*(v-2)) and see what happens there, or should
i use a more sophisticated method?
or is there a more elementary method?

thank you!