Chapter 1, Problem 68RE

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Using the Intermediate Value Theorem Use the Intermediate Value Theorem to show that f ( x ) = x 2 + x − 2 has at least two zeros in the interval [ − 3 , 3 ] .

To determine

To Prove: show that the function f(x)=x2+x2 has at least two zeros in the interval [3,3] to use the Intermediate value theorem.

Explanation

Given: f(x)=x2+xâˆ’2 and the interval [âˆ’3,3]

Proof:

the given function f(x)=x2+xâˆ’2, f is continuous on the closed interval [âˆ’3,âˆ’1], As f(âˆ’3)=(âˆ’3)2+(âˆ’3)âˆ’2=4 and f(âˆ’1)=(âˆ’1)2+(âˆ’1)âˆ’2=âˆ’2.So f(âˆ’3)>0 and f(âˆ’1)<0.

Appling the Intermediate value theorem concludes that there must be some c in [âˆ’3,âˆ’1], such that f(c)=0, hence f has a zero in the closed interval [âˆ’3,âˆ’1]

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