   Chapter 10, Problem 5T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 4-6, use the function y = 3 x 5 − 5 x 3 + 2 .Find the points of inflection of this function.

To determine

To calculate: The points of inflection for the function y=3x55x3+2.

Explanation

Given Information:

The provided equation is y=3x55x3+2.

Formula used:

To find points of inflection,

1. Set the second derivative of the function to zero, f(x)=0, to find the values of x for which the function has points of inflection.

2. Substitute the values into f(x) and calculate the inflection points.

Calculation:

Consider the provided equation,

y=3x55x3+2

Calculate the first derivative of the given equation.

y=15x415x2

Differentiate with respect to x again,

y=60x330x=30x(2x21)

Factorize (2x21) and simplify,

30x(2x21)=30x×2(x212)=60x(x2(12)2)=60x(x12)(x+12)

Set y=0.

60x(x12)(x+12)=0

Thus, either 60x=0 or (x12)=0 or (x+12)=0.

First consider 60x=0.

Simplify for x.

60x=0x=0

Now, consider (x12)=0

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