The cost and revenue functions for a certain production facility are:
C(x) = {x^2} + 2\,\,{\rm{and}}\,\,R(x) = 2{x^2} - x, then the break-even points are ( - 1,3)\,\,\,{\rm{and}}\,\,\,(2, - 6).
false
those codes don't work here, I read that as:
C(x) = x^2 + 2
R(x) = 2x^2 - x
equate them:
2x^2 - x = x^2 + 2
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or x = -1
if x=2, y = 6
if x = -1, y = 3
you had (2,-6) , don't see how you got y = -6
C(x) can never be negative, you are adding +2 to a square of something.
False
To find the break-even points, we need to determine the values of x where the cost function (C(x)) is equal to the revenue function (R(x)). In other words, we want to find the values of x where C(x) = R(x).
Given that C(x) = x^2 + 2 and R(x) = 2x^2 - x, we can set them equal to each other:
x^2 + 2 = 2x^2 - x
Rearranging the equation, we get:
x^2 - 2x^2 + x - 2 = 0
Simplifying further:
-x^2 + x - 2 = 0
Now we have a quadratic equation in standard form. To solve for x, we can use factoring, completing the square, or the quadratic formula.
Let's use factoring:
(-x + 2)(x - 1) = 0
Now we have two possibilities:
1) -x + 2 = 0 --> x = 2
2) x - 1 = 0 --> x = 1
So, the break-even points are x = 2 and x = 1.