BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 25RE
To determine

To show: The roots of the given equation lie in the given interval.

Expert Solution

Explanation of Solution

Given information:

The equation and intervalis 2x3+x2+2=0,(2,1) .

Calculation:

Consider the equation.

  2x3+x2+2=0

Substitute x=2 in above equation.

  f(2)=2(2)3+(2)2+2=10

Substitute x=1 in above equation.

  f(1)=2(1)3+(1)2+2=1

Since, f(2)f(1) and f(2)<0<f(1) .

Thus, at least one root lie in the given interval.

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