document.write( "Question 573037: y=x(x-1)^3
\n" ); document.write( "maximum?
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Algebra.Com's Answer #368639 by htmentor(1343) $\"\"$ $\"About$

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The maximum value of this function is $\"infinity\"$ , since y grows without bounds with increasing x.
\n" ); document.write( "The minimum value is obtained when the derivative, dy/dx = 0:
\n" ); document.write( "dy/dx = 0 = (x-1)^3 + 3x(x-1)^2
\n" ); document.write( "Divide through be (x-1)^2 -> (x-1) + 3x = 0
\n" ); document.write( "4x - 1 = 0
\n" ); document.write( "x = 1/4
\n" ); document.write( "Putting this value in the original function gives y = (1/4)(-3/4)^3 = -27/256 ~ -0.105 \n" ); document.write( "

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