Question

How to solve #7

Suppose that /(x,y)=(x+y2)3. Find s. and at the port az) , supportait atturbanco nennt.yoy, tindhaw.th.he%.anda 7. in a certain suburban community, commuters have the choice of geting into the ity by bus or train. The demand for these modes of transportation variles with their cost Let /(P.,P) be the number of people who will take the train when p, i the price of the bus ride and py is the price of the train ride. Would you expo bepsitive or negathe? Hew abour 8. Find all points (x.y) where f(x,y)-a+7xy- 4y+x y has possible relative maximum or minimum valkes 9. Find all points (x, y, z) where f (x.ya)-S + 8x-ty + y, ri has possible relati" maim m or mininum value 10. Both first partial derivatives of ()yy are zero at the points (0.01, .1), and (-1, 1). Use the second derivative test (for multivariable functions) to determine the nature of fx.y) at each of these given points 11. Find all points (x,y) where f(x, y) 2+3xy + 5y has possible relative masimum or minimum values. Then, use the second-derivative test (for multivariable functions) to determine, if possible, the nature of f(x. y) at eath of these points If the second-derlvative test is inconclusive, explain why. 12. Use the second-derivative test (for multivariable functions) to find the dimensions of the rectangular box of least surface area that has a volume of 30D0 cubic inches 13. A monopolist manufactures and sels two competing products, land , that cost $30 and $20 per unit, respectively, to produce. The revenue from marketing x usits of product I and yunts of product ts R (х.y)-98r + 1 1 2 y-0.1 x:-004 xy-02y, use the second dnriatim test f for multivariable functions) te find the values of s and y that masimise the monopolist's profits

Answer 1

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