Question 79956
A quadratic equation (like the one you have here) forms a "U" or "n" shaped curve. For the "U" type, there is a minimum value at the bottom of the "U" and likewise for the "n" shape, there is a maximum value at the top of the "n".  The actual shape of the graph (ie a "U" or an "n" shape) depends on the rest of the numbers in the equation.
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At the minumum (OR MAXIMUM) value of a function, a tangent drawn across the curve at that point will be flat. Which is another way of saying the gradient of the curve at that point is zero.
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How to find gradients of curves ?  Take the first derivative  (ie "differentiate it")

so C = 4x^2 - 40x + 225 

dC/dx = 8x - 40

At the minimum point, dC/dx will equal zero, so :

0 = 8x - 40

So 8x = 40
Therefore x = 5 [thousand automobiles]   (ANSWER)
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Incidentally, how do we know that this gives a minimum cost and not a maximum one ?  If you differentiate the equation again you get d2C/dx2 = 8 which is positive. So it is a minimum.