Questions
If is a polynomial function and and then
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a
ϕ(x)≥0 ∀x≥1
b
ϕ(x)<0 ∀x≥1
c
ϕ(x)=0 ∀x≥1
d
none of these
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Correct option is A
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
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If , then g(x) is increasing in
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