Question

Suppose the cost of producing x crates of pencils is given by c(x)= 1/2x^2-10x+1000. How much does it cost to produce 100 crates of pencils? How many crates of pencils will minimize the production cost?

Answer 1

to find the cost of 100 crates, replace x with 100 in the formula.

Notice that this is the equation of a parabola. Its vertex (its lowest point) is the minimum cost. the x value of the vertex is -b/(2a)

Answer 2

so would the answers be 4100

Answer 3

and 2.5