Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises: 2

Answer

\[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10,58\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 4{x^3} + 5{x^2} + 6x - 7 \hfill \\ Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\ {f^,}\,\left( x \right) = \,{\left( {4{x^3} + 5{x^2} + 6x - 7} \right)^,} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ {f^,}\,\left( x \right) = 4\,\left( 3 \right){x^{3 - 1}} + 5\,\left( 2 \right){x^{2 - 1}} + 6\,\left( 1 \right) \hfill \\ {f^,}\,\left( x \right) = 12{x^2} + 10x + 6 \hfill \\ and \hfill \\ {f^{,,}}\,\left( x \right) = \,{\left( {12{x^2} + 10x + 6} \right)^,} \hfill \\ {f^{,,}}\,\left( x \right) = 24x + 10 \hfill \\ find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\ {f^{,,}}\,\left( 0 \right) = 24\,\left( 0 \right) + 10 = 10 \hfill \\ {f^{,,}}\,\left( 2 \right) = 24\,\left( 2 \right) + 10 = 58 \hfill \\ \end{gathered} \]
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.