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: 5

Answer

\[{f^{,,}}\,\left( 0 \right) = 6\,\,\,and\,\,\,{f^{,,}}\,\left( 2 \right) = 6\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 3{x^2} - 4x + 8 \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,function \hfill \\ {f^,}\,\left( x \right) = \,\,{\left[ {3{x^2} - 4x + 8} \right]^,} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ {f^,}\,\left( x \right) = \,\,3\,\left( 2 \right){x^{2 - 1}} - 4\,\left( 1 \right) \hfill \\ {f^,}\,\left( x \right) = \,\,6x - 4 \hfill \\ Find\,\,the\,\,\sec ond\,\,derivative \hfill \\ {f^{,,}}\,\left( x \right) = \,\,{\left[ {6x - 4} \right]^,} \hfill \\ {f^{,,}}\,\left( x \right) = 6 \hfill \\ Then \hfill \\ {f^{,,}}\,\left( 0 \right) = 6\,\,\,and\,\,\,{f^{,,}}\,\left( 2 \right) = 6 \hfill \\ \end{gathered} \]
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