Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 16


$$ y=4x+1.$$

Work Step by Step

We have $$ y'=4e^{4x}\Longrightarrow y'(0)=4.$$ Then the slope of the tangent line at $ x=0$ is $ m= 4$. Hence the equation of the tangent line is given by $$ y=mx+c=4x+c.$$ Since $ y(0)=1$, then $ c=1$, hence the tangent line at $ x=0$ is given by $$ y=4x+1.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.