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Lecture

# 157IQsol9.pdf

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School
Simon Fraser University
Department
Mathematics
Course
MATH 157
Professor
Stephen Choi
Semester
Fall

Description
MATH 157 - D100A SSIGNMENT #9 Due date: Wednesday Mar 28, 2012 Instructor Questions accompanying paper Assignment # 9 Solution Directions: Print double sided, write your solutions to both questions directly on this page, place immediately after cover page and staple together! Marks: An answer without a detailed solution process will be awarded zero marks! Q1: Determine where the function is concave upward and where it is concave downward x + 1 f(x) = : x ▯ 1 Solution: Since 0 (x ▯ 1) ▯ 1 ▯ (x + 1) ▯ 1 ▯2 f (x) = (x ▯ 1)2 = (x ▯ 1)2 < 0: and 4 f"(x) = ; (x ▯ 1)3 so f"(x) > 0 on (1;1) and f"(x) < 0 on (▯1;1). Therefore f(x) is concave upward on (1;1) and concave downward on (▯1;1).
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