Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 47

Answer

$x=0$ and $x=\dfrac{4}{3}$

Work Step by Step

$4x^{3}e^{-3x}-3x^{4}e^{-3x}=0$ Take out common factor $x^{3}e^{-3x}$: $x^{3}e^{-3x}(4-3x)=0$ Set all three factors equal to $0$ and solve each individual equation: $x^{3}=0$ Take the cubic root of both sides: $\sqrt[3]{x^{3}}=\sqrt[3]{0}$ $x=0$ Move on to the second equation: $e^{-3x}=0$ No value of $x$ makes this second equation true. It has no solution. Move on to the third and final one: $4-3x=0$ Solve for $x$: $3x=4$ $x=\dfrac{4}{3}$ Our two solutions are: $x=0$ and $x=\dfrac{4}{3}$
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