Polynominals

[stormswimmer]

Here is the problem verbatim:

Profit: For the product is the previous exercise the demand function is p(x) = 330 + 10x - x[sup:2rfpg3ve]2[/sup:2rfpg3ve] Find the value of x for which the profit is $910.

The Previous Problem Reads:

Cost Function: The total cost of a product (in dollars) is given by C(x) = 3x[sup:2rfpg3ve]3[/sup:2rfpg3ve]-6x[sup:2rfpg3ve]2[/sup:2rfpg3ve]+108x+100, where x is the demand for the product. Find the value of x for which the total cost is 628 dollars.

I started by setting the equation = to 910

-x[sup:2rfpg3ve]2[/sup:2rfpg3ve]+10x+330=910
x[sup:2rfpg3ve]2[/sup:2rfpg3ve]-10x=-580

Where do I go next?

 

[mmm4444bot]

Here is the problem verbatim:

… the demand function is p(x) = 330 + 10x - x[sup:3q17to39]2[/sup:3q17to39] Find the value of x for which the profit is $910 …

Verbatim?

Are you sure that they told you p(x) represents demand, not profit?

I would think that a demand function gives demand, but they already told you that the variable x represents demand, so it's confusing to state that p(x) is a demand function.

-

… I started by setting the equation = to 910

-x[sup:3q17to39]2[/sup:3q17to39]+10x+330=910

x[sup:3q17to39]2[/sup:3q17to39]-10x=-580

If p(x) is actually the profit function (instead of some demand function), then you made a good start.

However, instead of subtracting 910 from both sides, I would have subtracted 330 from both sides because this gives a quadratic polynomial equal to zero. When you have a quadratic polynomial equal to zero, you can use the quadratic formula.

(You can accomplish this right now by continuing where you left off. Add 580 to both sides.)

So, you've got an equation in the form of ax^2 + bx + c = 0.

Have you learned anything about the quadratic formula?