Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 5.3, Problem 18E

To determine

To find all the points of inflection of the function

Expert Solution & Answer

Answer to Problem 18E

The inflection point is (1,4)

Explanation of Solution

Given Information:

Given function is,

Y=x1/2(x+3)

Calculation:

A point where the graph of a function has a tangent line and where the concavity changes is a point of inflection.

y1=32x1/2+32x1/2y11=34x−1/2−34x−3/2=34(1x1/2−1x3/2)∴y11=01x3/2−1x3/2=0⇒x3/2−1/2=1∴x=1interval(0,1) interval(1,∞)y11(0.5)≈−1⋅06<0 y11(2)≈0⋅27>oconcave down concave up

Concaving changes only at x=1 so there is one inflection point

y=(1)=1(1+3)=4

Put, x=0, into the original equation to find the Y value of the point

Hence,

The inflection point is (1,4)

Chapter 5.3, Problem 17E

Chapter 5.3, Problem 19E

Chapter 5 Solutions

Calculus: Graphical, Numerical, Algebraic

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