The management of acrosonic plans to market the electrostat, an electrostatic speaker system. the marketing department has determined that the demand for these speakers is represented by the following function, where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded.
p = -0.03x + 820 (0 x 20,000)
(a) find the revenue function r.
(b) find the marginal revenue function r'(x).
(c) compute the following value.
r'(5600) =

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

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0