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# 微積分高手請進(英文)15點

【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

C（x）＝（3x＋2）/（x＋4）.

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）.

Rating
• Leslie
Lv 7

I

(1)

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)]

-----(A)

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

(2)

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

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

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

Prof'(10)= 90/121 - 10

II

(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)

III

(a)

(703 w)/h^2

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

= 154660/5476

= 28.24

(b)

24.9 = (703*W)/5476

So, W = (24.9*5476)/703

= 194

So, 220-194 = 6

(c)

B(h)=(703*125)/h^2

B'(h)=(-2)*(703*125)/h^3

(d)

對不起, 題中根本沒 f, 何來 f'?

Source(s): CALCULUS textbook