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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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Optimizaion

also put like x-axis as my guide. The example is on 2nd pic

CONCAVITY and POINT of INFLECTION
ENG 203: DIFFERENTIAL CALCUĻUS
Concavity and Point of Inflection
2. y = x4 – 4x3
y" = 12x2 – 24x
yll
+
+
critical numbers of y' 0,2
2
Scroll for details
5:15 / 8:54
FACULTY OF ENGINEERING, UNIVER OFNTO TTMAS

CONCAVITY and POINT of INFLECTION
ENG 203: DIFFERENTIAL CALCULUS
Find all intervals for which the graph of y is concave upward/downward
and points of inflection
EXERCISE
ANSWERS
1. y = x³ –x?
concave up: (;, 0) ; concave down : (-∞,÷) ; POI: (÷,-→)
2. y = x³ – 3x2 + 3 x
concave up: (1, 0); concave down : (-o, 1); POI: (1,1)
3. y = 2x3 – 3x² – 36x + 14
concave up: (5, 0) ; concave down :(-,-); POI: (÷,-)
FACULTY OF ENGINEERING, UNIVERSITY OF SANTO TOMAS

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