Avehicle factory manufactures cars. the unit cost c (the cost in dollars to make each car) depends on the number of cars made. if x cars are made, then the unit cost is given by the function c(x) = x^2 - 400x + 45,377 . what is the minimum unit cost?
do not round your answer.

The minimum unit cost is 5377

Step-by-step explanation:

Note that we have a cudratic function of negative principal coefficient.

The minimum value reached by this function is found in its vertex.

For a quadratic function of the form

the x coordinate of the vertex is given by the following expression

In this case the function is:

So:

Then the x coordinate of the vertex is:

So the minimum unit cost is:

5377

Step-by-step explanation:

C(x) = x^2 - 400x + 45,377

To find the location of the minimum, we take the derivative of the function

We know that is a minimum since the parabola opens upward

dC/dx = 2x - 400

We set that equal to zero

2x-400 =0

Solving for x

2x-400+400=400

2x=400

Dividing by2

2x/2=400/2

x=200

The location of the minimum is at x=200

The value is found by substituting x back into the equation

C(200) = (200)^2 - 400(200) + 45,377

           =40000 - 80000+45377

            =5377