Questions: #8, 9, 12-17, 21-23

9. 10. 11. 12. 13. 14. 15. 16. 17. value of g the fastest? What is the directional derivative In this direction? Consider a box Whose side lengths are changing according to the vector function (,L W H): (5 t2, t3 How fast is the volume of the box changing when t 2? If f(:r,y) = 2231; + 31 y2 and :c(u,v) = Bu v2 and y(u.,v) = 21w, then calculate fu and f1, when u = 2 and v = 1. 4 2 Find and classify the critical points for f (1', y) = 8:53; :L' 2y . Let g(:c, y) = $2 + y2 + 29: 2y. Find the minimum and maximum values of g on the top half of the disk Where m2 + y2 S 9 and y 2 0. Let h(zr:, y) = any 2332. Find the minimum and maximum values of h on the rectangle Where 0 S a: S 1 and 0 S y S 2. Let f (as, y) = my. Find the minimum and maximum values on the part of the circle 3:2 + y2 = 4 from (2,0) to (1,\\/), traveling counter-clockwise. Let f (23, y, z) = 29: +41; 42. Find the minimum and maximum values of this function out of all points which are 1 unit from the origin. The production of a company with as units of supplies of type 1 and y units of supplies of type 2 can product P(a:, y) = ccy2 boxes of goods. Now type 1 supplies cost $2 per unit and type 2 supplies cost $6 per unit, and we only have a total budget of $36 for supplies this month. What is the maximum number of boxes of good we can produce this month? Give the dimensions of a box with 5 sides that has a surface area of 300 cm2 and holds the largest 2t,1 + 315). J0 J21: 1+?!\" 21. Let T be a thin metal plate lying on the trapezoidal region with vertices (2,0), (1, 1), (1, 1), and (2, 0) (with distances in cm). The density of the plate is given by the function p(9:, y) = 5 + x2 + myz, in g/cmz. Calculate the mass of the metal plate. 22. Let Q be the the region in the rst quadrant inside of a circle centered at the origin. If we know that ff my 01A 2 10, then what was the radius of the circle? Q 23. Calculate the volume of the region bounded by z = y2, at = 0, a: = 4, and z = 1