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: 55

Answer

$f(0) = -2$ $f(1) = 1.7$

Work Step by Step

$e^{x} = 3 - 2x$ $e^{x} -3 + 2x = 0$ Equal this fuction to $f(x)$. Now equal the value of $x$ to the values given in the interval: $(0,1)$. $f(0) = e^{0} -3 + 2(0)$ $= 1 - 3 = -2$ $f(1) = e^{1} -3 + 2(1) = e^{1} - 2 = 1.7$ The intermediate value theorem takes all the values between $f(0)$ and $f(1)$. So in this case $f(x)$ will take all the values between $-2$ and $1.7$.
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