Anonymous asked in 科學數學 · 1 decade ago



【一】(1)If the price in dollars of a stereo system is given by

P(q)=1000/(q² +1000),

Where q represents the demand for the product,

find the marginal revenue

when the demand is 10.

(2)承第一小題,the cost in dollars of producing q stereo

systems is given by

C(q)=0. 2q² +6q+50.

Find the marginal profit when the demand is 10.

【二】The total cost (in hundreds of dollars)to produce x units of perfume is


Find the average cost for each production level.

a. 10 units b. 20 units c. x units

d. Find the marginal average cost function.

【三】The body mass index (BMI)is a number that can be

calculated for any individual as follows:Multiply weight (lb)

by 709 and divide by the person’s.Height (in)squared.

That is BMI=(703w)/h²,

where w is in pounds and h is in inches. The National Heart,Lung,and Blood Institute uses the BMI to determine whether a person is

overweight(25≦BMI<30)or obese(BMI≧30)

a.Calculate the BMI for a person who weighs 220lb and is

6’2” tall .

b.How much weighs would the person in part a have to lose until

he reaches a BMI of 24.9 and is no longer overweight?

c.For a 125-lb female,what is the rate of change of BMI with

respect to height?

d.Calculate and inpret the meaning of f’(65).

1 Answer

  • Leslie
    Lv 7
    1 decade ago
    Favorite Answer



    R(q) = q*P(q)

    R'(q) = P(q)+q*P'(q)

    = [1000/(q^2+1000)]+q*[1000/1000 (-1)(2q)(q^2+1000)^(-2)]


    R'(10) = [10/11]+(10)[-2/121] = 90/121


    Prof(q) = R(q)-C(q)

    Prof'(q) = R'(q)-C'(q)

    = (A) - [(0.2)2q+6]

    Prof'(10)= 90/121 - 10


    (a) C(10)/10 = 0.22857

    (b) C(20)/20 = 0.12917

    (c) C(x)/x = (3x+2)/(x^2+4x)

    (d) (C(x)/x)' = [3(x^2+4x)-(3x+2)(2x+4)]/(x^2+4x)^2

    = (-3x^2-4x-8)/((x^2+4x)^2)



    (703 w)/h^2

    = (703*220)/(6*12+2)^2

    = 154660/5476

    = 28.24


    24.9 = (703*W)/5476

    So, W = (24.9*5476)/703

    = 194

    So, 220-194 = 6





    對不起, 題中根本沒 f, 何來 f'?

    Source(s): CALCULUS textbook
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