The profit function for a firm making dvds is p(x) = 88x - x2 -1200. find the number of dvds at which maximum profit is achieved, and find the maximum profit. explain your work.

This is a quadratic equation so you are looking for the vertex of the parabola.
The y value is the maximum profit.
p(x) = -x^2 + 88x - 1200
a = -1, b = 88
x = -b/2a; x = -88/(2*-1); x = 44
Plug x back in to the equation to find y.
y = -(44)^2 + 88(44) - 1200
y = 736
The number of DVD's sold were 44 for a profit of $736