the marginal revenue for x items in dollars is given by R'(x)=-2x+12 determine (a) the revenue function and b)the demand function
a)the revenue function is given by R(x)=
b)the demand function is given by p=
Given the marginal revenue, you can get the revenue by taking the integral of R'(x).
R'(x)= -2x + 12
`a)int R'(x) = int (-2x + 12)`
You may apply the Power Formula: `int u^n = (u^(n+1))/(n+1)`
The Revenue is:
`R(x) = (-2*x^(1+1))/(1+1) + (12*x^(0+1))/(0+1)`
`R(x) = -(2x^2)/2 + 12x`
`R(x) = -x^2 + 12x`
For the second question, recall that revenue = x * q.
where qis the quantity demand and x is the unit price.
So to get the demand function, factor out x.
`b) -x^2 + 12 x = x(-x + 12)`
There for the demand function, q is `-x + 12.`