B. (Applied optimization) 1.! If a close tin can of volume 1611 in' is to be in the form of right circular cvlind er. Find the height and radius if the least amount of material is to he used in Its manufacture. 1.! A rectangular container with an open top has a volume of 511 cubic inchu. Also, the length of the rectangle should be twice Its width. Find the dimension of the box that will maximize its surface area. 3.: The us postal service will accept a cylindrical package for domestic shipment only:I if the sum of its length and its girth [distance around] does not exceed all inches. Find the dimensions of the package of maximum volume that can he sent. 1.: Suppose that two motorboats leave from the same point at the same time. If one travels north at 15 miles per hour and the other travels east at In miles per hour, how fast will the distance between them be changing after 2 hoursiI 2.: Oil is running into an inverted conical tank at Eltt m'fmin. If the tank has a radius of 1 meter at the top and a depth of 1i'.lm. How fast is the depth of the oil changing when it is 8 meter deep? Basic Calculus Activity A.) FIND THE DERIVATIVE (high order + implicit) x3-2 1.) y = 2x3+1 2.) y = 2xvx - 3 ; y" 3.) y = (2x3 + 5)4 ; y" 4.) y = 5.) Evaluate y" + 2y' + 2y when y = e-*sin(x) 1.) x 2 y + 2y3=3x + 2y ; y' 2.) x2 - 5xy + 2y2 = 4 ; y' 3.) # + = =2 ;y 4.) x + yln(x2) + 3y2 = 2x2 - 1 ; y' 5.) 4x2 = 3 + 7y2 ; y"