A firm has the marginal-demand function Upper D prime (x )equalsStartFraction negative 1200 x Over StartRoot 25 minus x squared EndRoot EndFraction . Find the demand function given that Dequals16 comma 000 when x equals $ 4 per unit.

The demand function is  

Step-by-step explanation:

A firm has the marginal-demand function .

Find the demand function given that D = 16,000 when x = $4 per unit.

What we are required to do  is to find the demand function D(x);

If we integrate D'(x) with respect to x ; we have :

Let represent   t  with

The differential of t with respect to x is :

replacing the value of    for dt in  

So; we can say :

Let's Recall that :

t  =

Now;

GIven that:

D = 16,000 when x = $4 per unit.

i.e

D(4) = 16000

SO;

16000 = 1200 (3) + C

16000 = 3600 + C

16000 - 3600 = C

C = 12400

replacing the value of C = 12400 into , we have:

∴ The demand function is  

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step-by-step explanation: