Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 13 - Section 13.1 - The Indefinite Integral - Exercises - Page 958: 46

Answer

$f(x)=2e^{x}+x-2e-2$

Work Step by Step

The tangent line at $(x, f(x))$ has slope $f'(x)$, which is given as: $f'(x)=2e^{x}+1$ So, $f(x)$ is an antiderivative: $f(x)=\displaystyle \int(2e^{x}+1)dx=2e^{x}+x+C.$ The indefinite integral gives us a collection of functions. To find the exact function, we find C. We are given that $f(1)=-1$, so $-1=2e^{1}+1+C$ $-2e-2=C$ So, $f(x)=2e^{x}+x-2e-2$
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