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# HW 7 - Math E-21a Fall 2009 HW#7 problems Problems to turn...

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1 Math E-21a – Fall 2009 – HW #7 problems Problems to turn in on Thurs, Oct 22 : Section 11.7 : In problems 6-14, find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. 6. 32 (, ) 1 2 8 f xy xy x y  10. 322 2 (, ) 2 5 x x y x y  12. 22 1 fxy x y x y  14. (, ) (2 ) (2 ) x x y y  26. Find the absolute maximum and minimum values of the function (, ) 3 2 x y x y  on the set D where D is the closed triangular region with vertices (1,0) ,(5,0) , and (1,4) . 34. Find the point on the plane 4 xyz  that is closest to the point (1,2,3) (using unconstrained calculus methods). 36. Find the points on the surface 2 9 y xz that are closest to the origin. 37. Find three positive numbers whose sum is 100 and whose product is a maximum. 39. Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 2 93 643 6 z  . [ Note : Do this using unconstrained calculus methods. You will do this same problem using the simpler Lagrange Multiplier method in Exercise 11.8/31 below.]

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HW 7 - Math E-21a Fall 2009 HW#7 problems Problems to turn...

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