The cost to produce a product is modeled by the function f(x) = 3x2 − 6x + 11 where x is the number of products produced. complete the square to determine the minimum cost of producing this product. 3(x − 1)2 + 8; the minimum cost to produce the product is $8. 3(x − 1)2 + 8; the minimum cost to produce the product is $1. 3(x − 1)2 + 11; the minimum cost to produce the product is $1. 3(x − 1)2 + 11; the minimum cost to produce the product is $11.

We will complete the square and find out what the vertex means to the problem. Start by setting the quadratic equal to 0 then move over the 11 by subtraction. That gives us . The rule for completing the square is that the leading coefficient has to be a 1. Ours is a 3, so we have to factor it out. . Now we will take half the linear term, square it, and add it to both sides. Our linear term is 2. Half of 2 is 1, and 1 squared is 1. So we add 1 inside the parenthesis on the left. But don't forget that 3 hanging around outside refusing to be ignored. It is a multiplier. What we have actually added in is 3 times 1 which is 3. So this is what that looks like: . On the right we simplify to -8 but on the right we have a perfect square binomial, which is the whole reason for what we have done. That perfect square binomial is . If we move the -8 over by addition we have . That tells us that the vertex is (1, 8). If x is the number of items produced and y is the cost, our vertex tells us that the minimum cost to produce that 1 (x) item is $8 (y). Your answer is the first one listed.

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

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