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Chapter 4: Q. 23 (page 245)

Use the Intermediate Value Theorem to show that each polynomial function has a zero in the given interval.

f(x)=3x3-x-1;[0,1]

Short Answer

Expert verified

The given function has a zero between 0 and 1

Step by step solution

01

Step 1. Given Information

The given function and the interval isf(x)=3x3-x-1;[0,1]

02

Step 2. Calculation

We will evaluate the function at 0 and 1.

f(0)=3(0)3-0-1=-1f(1)=3(1)3-1-1=1

Since, f(0)<0andf(1)>0andf(0)andf(1)are of opposite sign, it follows from the intermediate value theorem that the function has a zero between 0 and 1.

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