The marginal revenue for x items in dollars is given by R′(x)=−4.5x+6. Determine (a) the revenue function and (b) the demand function.
I know the revenue function is R(x)=6x-2.25x^2 just by finding the antiderivative. demand = revenue - cost, but how do I even find what the cost function is?
To determine the revenue function, we integrate the marginal revenue function, R'(x), with respect to x. The integral of -4.5x+6 with respect to x is -2.25x^2+6x+C, where C is the constant of integration. However, since we are looking for the revenue function, we set the constant of integration to 0, as it represents the revenue for x = 0 items (which is assumed to be 0).
So, the revenue function, R(x), is given by R(x) = -2.25x^2 + 6x.
Now, to find the demand function, we need to determine the cost function. The cost function represents the cost per unit to produce those items. However, the given information does not provide any explicit information about the cost.
Without additional information to directly calculate the cost function, we cannot determine it solely from the given marginal revenue function. It is possible that you may need to look for additional information elsewhere or assumptions need to be made to estimate the cost function.