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: 1

Answer

\[\,\,\,\,\,\,\,\,\,\,\, = - 14\,\,,\,\,46\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 5{x^3} - 7{x^2} + 4x + 3 \hfill \\ Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\ {f^,}\,\left( x \right) = \,{\left( {5{x^3} - 7{x^2} + 4x + 3} \right)^,} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ {f^,}\,\left( x \right) = 15{x^2} - 14x + 4 \hfill \\ and \hfill \\ {f^{,,}}\,\left( x \right) = \,{\left( {15{x^2} - 14x + 4} \right)^,} \hfill \\ {f^{,,}}\,\left( x \right) = 30x - 14 \hfill \\ find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\ {f^{,,}}\,\left( 0 \right) = 30\,\left( 0 \right) - 14 = - 14 \hfill \\ {f^{,,}}\,\left( 2 \right) = 30\,\left( 2 \right) - 14 = 46 \hfill \\ \end{gathered} \]
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