There are three ways. You can graph the function, you can put the quadratic in the general form of a parabola (which gives you the vertex, the lowest point on the parabola) or, since you are in Calculus you can take the first derivative of the cost function and set it equal to zero:Originally Posted bybret80

Thus

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To verify this is actually a relative minimum and not a relative maximum, apply the second derivative test:

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Since C'' is positive at x = 20 (in fact C'' is positive everywhere) x = 20 is a relative minimum.

-Dan