# How do you find the value of x that gives the minimum average cost, if the cost of producing x units of a certain product is given by #C = 10,000 + 5x + (1/9)x^2#?

##### 1 Answer

Your function is a quadratic and can be represented by a PARABOLA (basically the shape of an "U" upwards or downwards oriented).

Your parabola is in the shape of "U" because the coeficient of

You basically are looking for a **minimum** (the vertex) of your parabola (the bottom of your "U" shape) and the corresponding

To find this you have various methods:

1) plot your function and look for it;

2) using the fact that the vertex has coordinate

3) Derive your function and set the derivative equal to zero (this gives you the point of inclination equal to zero or your minimum).

I would use the derivative stuff:

Set it

You can check using method 2).

And Graphically: