document.write( "Question 106056: I am trying to sketch the graph TC = 0.2q^3 - 4q^2 + 28q (where TC is total cost and q is output). However, when I differentiated the equation to find the roots I obtained dTC/dq = 0.6q^2 - 8q + 28, which when substitued into the quadratic formula gives a -ve root (64-67.2), which in my undrestanding means there are no roots. What does the graph look like then?\r
\n" ); document.write( "\n" ); document.write( "Regards, John McGrory.\r
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Algebra.Com's Answer #77158 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
John,
\n" ); document.write( "You found the derivative correctly.
\n" ); document.write( "However, you cannot find the roots of an equation by finding the roots of the derivative.
\n" ); document.write( "The roots of the derivative can give you information about the minima and maxima of the function.
\n" ); document.write( "Here is the graph of the function and its derivative.
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\n" ); document.write( "You are also correct with regards to the derivative, its roots are complex, and the derivative is never equal to zero.
\n" ); document.write( "The function does have a zero at x=0.
\n" ); document.write( " $\"TC%28q%29=0.2q%5E3-4q%5E2%2B28q\"$
\n" ); document.write( " $\"TC%28q%29=q%280.2q%5E2-4q%2B28%29\"$
\n" ); document.write( "The roots of
\n" ); document.write( " $\"0.2q%5E2-4q%2B28\"$ are complex. There is only one real zero at x=0. \n" ); document.write( "

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