Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises - Page 180: 48

Answer

$f(x)=e^x-x^3$ $f'(x)=e^x-3x^2$ $f''(x)=e^x-6x$

Work Step by Step

Let's first remember the power rule: $f(x)=x^n$ $f'(x)=nx^{n-1}$ And we also know that $\frac{d}{dx}[e^x]=e^x$ So with this information, we can find the first and second derivatives. We know that $f(x)=e^x-x^3$ So by using the power rule and the differentiation of an exponential function, we can find that: $f'(x)=e^x-3x^2$ And by taking the derivative of that, we can find the second derivative: $f''(x)=e^x-6x$ So now you now that $f(x)=e^x-x^3$ $f'(x)=e^x-3x^2$ $f''(x)=e^x-6x$ You can graph each equation together to make sure these answers are reasonable.
Small 1504524047
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.