# Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises - Page 283: 3

$\,\,\,\,\,\,\,\,\,\,\,\, - 4,152$

#### Work Step by Step

$\begin{gathered} f\,\left( x \right) = 4{x^4} - 3{x^3} - 2{x^2} + 6 \hfill \\ Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\ {f^,}\,\left( x \right) = \,\,{\left[ {4{x^4} - 3{x^3} - 2{x^2} + 6} \right]^,} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ {f^,}\,\left( x \right) = 16{x^3} - 9{x^2} - 4x \hfill \\ Find\,\,{f^{\,,,}}\,\left( x \right) \hfill \\ {f^{\,,,}}\,\left( x \right) = \,{\left( {16{x^3} - 9{x^2} - 4x} \right)^,} \hfill \\ {f^{\,,,}}\,\left( x \right) = 48{x^2} - 18x - 4 \hfill \\ find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\ {f^{\,,,}}\,\left( 0 \right) = 48\,{\left( 0 \right)^2} - 18\,\left( 0 \right) - 4 = - 4 \hfill \\ {f^{\,,,}}\,\left( 2 \right) = 48\,{\left( 2 \right)^2} - 18\,\left( 2 \right) - 4 = 152 \hfill \\ \hfill \\ \end{gathered}$

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