A manufacturing co estimates that its profit, in hundreds of dollars, after producing x thousand units can be expressed as p= -x^2 +6x-1 How many units must be produced to obtain the maximum profit?

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The maximum or minimum value for a continuous function is where its derivative equals 0, or if you're only considering a certain interval such that there is no place the derivative is 0, then the minimum and maximum is at an end point.In this case:p=-x^2+6x-1dp/dx=-2x+60=-2x+6x=3