Mark left school and drove south at an average speed of 26 km/h. Sometime later
Alberto left driving in the same direction
but at an average speed of 65 km/h. After
driving for two hours Alberto caught up
with Mark. How long did Mark drive
before Alberto caught up?

a) R(x)  = -0.03*x² + 820*x

b) R´(x)  = -  0.06*x + 820

c) R´(5600)   = 484 units)

Step-by-step explanation:        

a) We have unit price of the product

p(x)   =  - 0,03*x + 820               where   0  ≤  x  ≤ 20000

Then Revenue Function

R(x)  = x*p(x)       ⇒  R(x)  = x* ( - 0.03*x + 820)

R(x)  = -0.03*x² + 820*x

b) The Marginal Revenue Function is:

We get derivatives to get that function

R´(x)  = -2*0.03*x  + 820

R´(x)  = -  0.06*x + 820

c) Compute

R´(5600) ??

R´(x)  = -  0.06*x + 820

for x = 5600

R´(5600)   =  -0.06 ( 5600) + 820

R´(5600)   = 484 units