document.write( "Question 414181: Find all of the critical points for f(x).
\n" ); document.write( "f (x) = x^3 + 10x^2 + 25x - 50
\n" ); document.write( "One critical point is (-5/3, -1850/27).
\n" ); document.write( "What is the remaining critical point? \n" ); document.write( "

Algebra.Com's Answer #290515 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
The derivative of f(x) is given by\r
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\n" ); document.write( "\n" ); document.write( " $\"%28d%2Fdx%29f%28x%29+=+3x%5E2+%2B+20x+%2B+25\"$ (applying the power rule)\r
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\n" ); document.write( "\n" ); document.write( "The critical points occur when $\"%28d%2Fdx%29f%28x%29+=+0\"$ , i.e.\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2+%2B+20x+%2B+25+=+0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-20+%2B-+sqrt%28400+-+300%29%29%2F6+=+%28-20+%2B-+10%29%2F6\"$ = -5/3 and -5. f(5) = -125 + 250 + (-125) - 50 = -50, so (-5, -50) is the other critical point (sorry I accidentally replaced -5 into f'(x) instead of f(x) so I just revised my answer). \n" ); document.write( "

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