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$If f (1) = 0 and \frac{d f}{d x} > f (x) \forall x \geq 1, then$

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fx>0

fx>1

fx>e

fx>1e

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Correct option is A

dfdx−f(x)>0⇒e−xdfdx−f(x)>e⇒ddxe−x⋅f(x)>0⇒e−x⋅f(x) is on increasing function f(1)=0→e−x⋅f(x)>0→f(x)>0

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If f(1)=0 and dfdx>f(x)∀x≥1 , then

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$If f (1) = 0 and \frac{d f}{d x} > f (x) \forall x \geq 1, then$