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

Correct option is 1ϕ(x)≥0 ∀x≥1

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If $ϕ (x)$ is a polynomial function and $ϕ^{'} (x) > ϕ (x) \forall x \geq 1$ and $ϕ (1) = 0,$ then

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ϕ(x)≥0 ∀x≥1

ϕ(x)<0 ∀x≥1

ϕ(x)=0 ∀x≥1

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detailed solution

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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If $ϕ (x)$ is a polynomial function and $ϕ^{'} (x) > ϕ (x) \forall x \geq 1$ and $ϕ (1) = 0,$ then