Question

Find the demand function for the marginal revenue function. Recall that if no items are​ sold, the revenue is 0.

Answer 1

The integral that is needed to solve the demand function is R(x) = 599x - 0.14$x^{3/2}$

What is Demand Function?

A demand function describes the mathematical relationship between the quantity demanded and one or more determinants of the demand, as the price of the good or service, the price of complementary and substitute goods, disposable income, etc.

Here, given differential equation;

R'(x) = 599 - 0.21$\sqrt{x}$

we can also write this as;

$\frac{d}{dx}R(x) = 599 - 0.21\sqrt{x}$

$d R(x) = (599 - 0.21\sqrt{x} ) dx$

On integrating both sides, we get

$\int\ d R(x) = \int\ (599 - 0.21\sqrt{x} ) dx$

R(x) = $599x - 0.21 X \frac{2}{3}x^{3/2}$ + C

R(x) = 599x - 0.14$x^{3/2}$ + C       ...........(i)

Also given, at x = 0, R(x) = 0, Put these values in equation (i), we get

0 = 0 - 0 + C

C = 0

Put the value of C in equation (i), we get

R(x) = 599x - 0.14$x^{3/2}$

Thus, the integral that is needed to solve the demand function is R(x) = 599x - 0.14$x^{3/2}$

Learn more about Demand Function from:

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