Answer to Question #41714 in Real Analysis for Abdul

Question #41714
Assume a = a(t) ∈ L1(0,1)∩C(0,∞), ∞ ≥ a(0+) > a(∞) ≥ 0 and a(t) ≥ 0, a′(t) ≤ 0, a′′(t) ≥ 0, a′′′(t) ≤ 0, on (0,∞). Let h(t) = ta(t) on (0,∞). Then one of the following is true. There exists a number ε > 0 such that h is increasing on (0, ε). Or, there is no such interval. Which is correct? Prove it.
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Expert's answer
2014-05-12T08:11:00-0400
The answer to the question is available in the PDF file https://www.assignmentexpert.com/https://www.assignmentexpert.com/homework-answers/mathematics-answer-41714.pdf

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