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If P(1)=0a n d(d P(x))/(dx)>P(x) for all...

If `P(1)=0a n d(d P(x))/(dx)>P(x)` for all x>=1. Prove that P(x)>0 for all x>1

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To prove that \( P(x) > 0 \) for all \( x > 1 \) given that \( P(1) = 0 \) and \( \frac{dP(x)}{dx} > P(x) \) for all \( x \geq 1 \), we can follow these steps: ### Step 1: Understand the given conditions We know that: 1. \( P(1) = 0 \) 2. \( \frac{dP(x)}{dx} > P(x) \) for all \( x \geq 1 \) ### Step 2: Rewrite the inequality ...
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