Chapter 4: Q. 24 (page 245)

Use the Intermediate Value Theorem to show that each polynomial function has a zero in the given interval.
$f (x) = 8 x^{4} - 4 x^{3} - 2 x - 1; [0, 1]$

Short Answer

Expert verified

The given function has a zero between 0 and 1

Step by step solution

Step 1. Given Information

The given function and the interval is $f (x) = 8 x^{4} - 4 x^{3} - 2 x - 1; [0, 1]$

Step 2. Calculation

We will evaluate the function at 0 and 1.

$f (0) = 8 {(0)}^{4} - 4 {(0)}^{3} - 2 (0) - 1 = - 1 f (1) = 8 {(1)}^{4} - 4 {(1)}^{3} - 2 (1) - 1 = 1$

Since, $f (0) < 0 a n d f (1) > 0 a n d f (0) a n d f (1)$ 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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Use the Intermediate Value Theorem to show that each polynomial function has a zero in the given interval.
$f (x) = 8 x^{4} - 4 x^{3} - 2 x - 1; [0, 1]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Use the Intermediate Value Theorem to show that each polynomial function has a zero in the given interval.f(x)=8x4-4x3-2x-1;[0,1]

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Logic and Functions

Probability and Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Use the Intermediate Value Theorem to show that each polynomial function has a zero in the given interval.
$f (x) = 8 x^{4} - 4 x^{3} - 2 x - 1; [0, 1]$