SOLUTION: 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 =

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?
Regards, John McGrory.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
John,
You found the derivative correctly.
However, you cannot find the roots of an equation by finding the roots of the derivative.
The roots of the derivative can give you information about the minima and maxima of the function.
Here is the graph of the function and its derivative.

You are also correct with regards to the derivative, its roots are complex, and the derivative is never equal to zero.
The function does have a zero at x=0.

The roots of
are complex. There is only one real zero at x=0.
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