document.write( "Question 220705: For what values of x does the graph of f(x) = 2x^3 - 3x^2 - 6x + 51 have a horizontal tangent?
\n" ); document.write( "smaller and larger values?
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Algebra.Com's Answer #165623 by stanbon(75887) $\"\"$ $\"About$

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For what values of x does the graph of f(x) = 2x^3 - 3x^2 - 6x + 51 have a horizontal tangent?
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\n" ); document.write( "Take the derivative; set it to zero; solve for \"x\".
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\n" ); document.write( "f'(x) = 6x^2-6x-6 = 0
\n" ); document.write( "x^2-x-1 = 0
\n" ); document.write( "x = [1 +- sqrt(1-4*1*-1)]/2
\n" ); document.write( "x = [1 +- sqrt(5)]/2
\n" ); document.write( "x = (1+(sqrt(5))/2 or (1-(sqrt(5))/2
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\n" ); document.write( "Let's see what it looks like:
\n" ); document.write( " $\"graph%28400%2C300%2C-10%2C10%2C-60%2C60%2C2x%5E3-3x%5E2-6x%2B51%29\"$
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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