document.write( "Question 1032465: f(x)= x^3-3x^2-9x+5
\n" ); document.write( "find and classify all stationary points.\r
\n" ); document.write( "\n" ); document.write( "sketch the graph of fx. \n" ); document.write( "

Algebra.Com's Answer #648226 by robertb(5830) $\"\"$ $\"About$

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$\"f%28x%29=+x%5E3-3x%5E2-9x%2B5\"$ ==> f'(x) = $\"3x%5E2-6x-9+=+3%28x%5E2-2x-3%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "The stationary points are where f'(x) is zero.\r
\n" ); document.write( "\n" ); document.write( "Hence let $\"x%5E2-2x-3+=+%28x-3%29%28x%2B1%29+=+0\"$ .\r
\n" ); document.write( "\n" ); document.write( "==> x = 3, -1.\r
\n" ); document.write( "\n" ); document.write( "Now f\"(x) = 6x-6 ==> f\"(3) = 12 > 0 ==> local min at x = 3.\r
\n" ); document.write( "\n" ); document.write( "f\"(-1) = -12 < 0 ==> local max at x = -1.\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28+500%2C+500%2C+-15%2C+15%2C+-25%2C+20%2C+x%5E3-3x%5E2-9x%2B5%29\"$ \n" ); document.write( "

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