If ϕ(x) is a polynomial function and ϕ′(x)>ϕ(x)  ∀x≥1 and ϕ(1)=0,then

Given ϕ′(x)−ϕ(x)>0 ∀x≥1or      e−xϕ′(x)−ϕ(x)>0 ∀x≥1or     ddxe−xϕ(x)>0 ∀x≥1Therefore,  e−xϕ(x)) is an increasing function ∀x≥1.Since ϕ(x) is a polynomial,       e−xϕ(x)>e−1ϕ(1) or e−xϕ(x)>0 [∵ϕ(1)=0]or    ϕ(x)>0