1. The sum of three positive numbers is 30. The first plus twice the
second plus three times the third add up to 60. Select the numbers so that the product of all three is as large as possible.
2. Determine the intervals on which the following functions are
increasing or decreasing and find also the local maximum or
minimum:
(a) f(X) = 2x^2– ln X , X > 0
(b) f(X) = 2x^3 – 9x^2– 24X + 7
3. The total cost of producing x radio sets per day is $(1/4x2 + 35x +25) and the price per set at which they may be sold is $(50 – x/2). What should be the daily output in order to obtain a maximum total profit? Find also the corresponding profit.
4. Find dy/dx for each of the following functions:
(a) y =5x^3-x^(-2/5)
(b) y = (√x (2-x^2))/x
(c) y = (√x-3x+1)(∜x-2√x) <--4開方X
(d) y =∛((8x^2-3)/(x^2+2)) <--3開方X
(e) y = √((x-1)(x+2)^3 )作者: Naozumi 時間: 11-3-2 08:32 AM
Q1
let x , y and z be the first, the second and the third number respectively.
x + y + z = 30 ....(1)
x + 2y + 3z = 60 ....(2)
(1) x 2 - (2): z = x
Put x = 2z into (1), y = 30 - 2x
define P = xyz
Then P = x(30 - 2x)x = x^2 (30 - 2x)
剩番果d只係普通differentitation的問題作者: PinkyPYC 時間: 11-3-5 12:32 PM