Explanation Given: h ( x ) = 2 ln x − x 2 at x = 1 . Concept used: f " ( x ) is positive, the given function is concave up. f " ( x ) is negative, the given function is concave down. Calculation: h ( x ) = 2 ln x − x 2 h ' ( x ) = 2 ( 1 x ) − 2 x = 2 ( x ) − 1 − 2 x h ' ' ( x ) = 2 ( − 1 ) x − 2 − 2 h ' ' ( x ) = − 2

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

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Chapter 3, Problem 15SYU

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Whether the given statement is true or false.

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Chapter 3, Problem 14SYU

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APPLIED CALCULUS-WILEYPLUS

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To check: Whether the given statement is true or false.

Solution Summary: The author explains that f(x) is positive, the given function is concave up.