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Found problems: 1

2005 Gheorghe Vranceanu, 2
Tags: real analysis , asymptote , linear polynomial , polynomial , algebra
Let be a twice-differentiable function $ f:(0,\infty )\longrightarrow\mathbb{R} $ that admits a polynomial function of degree $ 1 $ or $ 2, $ namely, $ \alpha :(0,\infty )\longrightarrow\mathbb{R} $ as its asymptote. Prove the following propositions: [b]a)[/b] $ f''>0\implies f-\alpha >0 $ [b]b)[/b] $ \text{supp} f''=(0,\infty )\wedge f-\alpha >0\implies f''=0 $