Multiple Integrals and Rate of Change
Can anyone help me with these problems?
1)Freddy sells ice cream. Starting on Mon at 10am he sells only 1 bucket per hour and it increases quadratically with time to 4pm when his sales peak to 25 buckets per hour. After that it slows down linearly to 2 buckets per hour at 9pm. He works with this pattern on MWF(he is off Tue and Thur) and on Sat and Sun the sales double with the same pattern. Use a multiple integral and direct calculation to find the total sales volume.
2)Two mice start pulling the points (1,2,0) and (2,0,1) in the directions of OM and ON resp. at the rate of 5 units per second. Find the rate of change of the volume of the parallelpipped built with OM, ON, and OP. (point M(1,2,0) N(2,0,1) P(1,2,3) and 0(0,0,0) )
3)A robot has landed on the 500-level-surface of f has enough energy to take 5 steps of size 2 units. Starting form the point P(4,-5,?). What is the maximum height it can reach? find the coordinates of all the intermediate steps. (let f(x,y,z)=2x+xy^3-zx^2)