Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 53

Answer

There is a root in the specified interval.

Work Step by Step

$f(x) = x^{4} + x - 3$ Use the numbers of the given interval: $(1,2)$ $f(1) = 1^{4} + 1 - 3 = -1$ $f(2) = 2^{4} + 2 - 3 = 15$ From this we know that $f(x)$ is a continuous function in the given interval. By the definition of the Intermediate Value Theorem $f(x)$ will take all the values between $-1$ and $15$. So there is at least one value of $x$ for which $f(x)$ is zero. So there is at least one root of $f(x) = 0$ in the interval $(1,2)$.
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