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1) Differentiate the following functions, (a) f(x)=1/5 x^5-1/3 x^3+5 (c) y=(3x^2-9)/x (c) y = ln ?(3x^5+8x-5)?^2 2. Find the critical points for y=x^3-3x+1 and determine whether the critical points are minimum, maximum or inflection. 3. Entrepreneur of a product estimates that when q units of his items produced every month, the average total profit (in thousand RM) is P ¯(q)= -1.125q+45-200/q. Find the company's maximum profit. 4. Given f(x,y)=3x^3 y^2. Then find: (i) f_x (-1,2) (ii) f_y (-2,1) 5. Using LaGrange Multipliers, find x and y that will maximize f(x,y)=3x^2+xy+2ysubject to the constraint x + y = 200. 6. Integrate: (a) ∫¦?2x(x^2-3)^5 ?dx (b) ∫_4^10¦√(5x+1 ) dx 7. The demand functions for a product is given by p=200-q^2, where p is the price per unit and q is the quantity. If the supply function is given by p=6q+160, find the consumer's surplus and producer's surplus under market equilibrium.
The revenue from marketing x units of product I and y units of product II is 105x + 121y - .04xy - .1x2 - .2y2. Find the values of x and y that maximize the monopolist's profits.
the central ohio paper company wants to estimate the mean time required for a new machine to produce a ream of paper
On a nationwide test taken by high school students, the mean score was 49 and the standard deviation was 11.The scores were normally distributed. Approximately how many of the students scored between 16 and 82.
four pairs of data yield r=0.942 and the regression equation y = 3x. also, y = 12.75. what is the best predicted value of y for x = 2.9?
the laser used in a compact disc player has a time to failure which follows an exponential distribution with a mean of
A company wishes to manufacture a box with a value of 28 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minumum amount of material.
use an n-tuple integral to find the volume enclosed by a hypersphere with radius r in n-dimensional space.
hoping to lure more customers to the downtown area the city council has voted to build a new parking garage. they plan
A windshield wiper that is 2 feet long sweeps through an angle of 157°. What is the distance traveled by the tip of the wiper?
What will it cost Downhill Boards to outsource the finishing process?
if the given external source is replaced by a force of 2 cos wt of frequency w, find the value of w for which the amplitude of the force response is maximum.
Explain in your own words how the principle of square roots is used to solve quadratic equations. What form must a quadratic equation be in to use the principle of square roots for solving? Demonstrate the process with your own example.
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