60 points

the revenue r (in thousands dollars) for a business is modeled by the equation , where x is the number of years since 2000. the cost c (in thousands dollars) for this business is modeled by the equation .

which equation represents the profit, p, for this business?

Profit would be the revenue minus the cost

 so R=x^3-6x^2 +x +75 - C=x^2-70x =

see picture for answer

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204