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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
a rectangular storage container with an open top has a volume of 10 m3. the length of its base is twice its width.
In your own words, explain the process of multiplying and dividing polynomial. How are they similar? Why is adding and subtracting polynomials so different?
The cost of producing x units of a product is given by C(x)=600 + 120 x - 120 ln(x), Find the minimum average cost.
Optain the academic standards for kindergarten for three states (available on state education websites). Compare the standards in a single category such as math or reading and describe how the standards are similar or different across the states.
Write a differential equation for the total quantity of dead leaves (per square centimeter) at time t.
the function f is defined by fx x -1. sketch its graph. observe that there is no value c such that f3-f0 fc3-0. why
Determine the expected payoff of the game
Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using What is the value of the test statistic?
Because the sample size is small, we must verify that reading speed is normally distributed and the sample does not contain any outliers. The normal probability plot and boxplot are shown. Are the conditions for testing the hypothesis satisfied?
Probability Based on Order and Random Selection, Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely,
A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 186 square feet?
When graphing a linear inequality, how do you select the area (which side of the line) that is being represented (and has to be shaded) by the inequality?
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