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 - Page 283: 6

Answer

\[{f^{,,}}\,\left( 0 \right) = \,16\,\,\,\,\,and\,\,\,\,{f^{,,}}\,\left( 2 \right) = 16\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 8{x^2} + 6x + 5 \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,function \hfill \\ {f^,}\,\left( x \right) = \,\,{\left[ {8{x^2} + 6x + 5} \right]^,} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ {f^,}\,\left( x \right) = 16{x^{2 - 1}} + 6\,\left( 1 \right) \hfill \\ {f^,}\,\left( x \right) = 16x + 6 \hfill \\ Find\,\,the\,\,\sec ond\,\,derivative \hfill \\ {f^{,,}}\,\left( x \right) = \,\,{\left[ {16x + 6} \right]^,} \hfill \\ {f^{,,}}\,\left( x \right) = 16 \hfill \\ Then \hfill \\ {f^{,,}}\,\left( 0 \right) = \,16\,\,\,\,\,and\,\,\,\,{f^{,,}}\,\left( 2 \right) = 16 \hfill \\ \end{gathered} \]
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.