Help plz. Write it on a paper with correct solutions.

5. b) A cylindrical chemical storage tank with a capacity of 4000 m3 is going to be constructed. The specifications call for the base to be made of sheet steel that costs $100/m?2, the top to be made of sheet steel that costs $50/m2, and the wall to be made of sheet steel that costs $70/m?2. Determine the proportions that minimize the cost of the steel for construction. [10 marks] A drug is injected into the body in such a way that the concentration, C, in the blood at time hours is given by the function C(r)=10( "). At what time does the highest concentration occur? [6 marks] At what time does the concentration level start to decrease at a decreasing rate? [4 marks] 7. The graph of y = f'(x) is shown to the right. ? a) State the intervals of increase and decrease for y = f(x). [3 marks] b) From the above info, what is the x-value ! of the local maximum and minimum of y = f(x)? [2 marks] \\ 3 8. The graph of y = g'(x) is shown to the right. \\ a) State the intervals of concavity for y = g(x). [2 marks] \\ , b) What is the x-value of the point of inflection of y = g(x)? \\ [2 marks] \\ 1 \\ 3 2 | of 1 2 3 4x 9 If f(x)=7F.. 4(x +1) and f(x) = 8(x+2) (x -1 (x-1) b) Use the function and its derivatives to determine the domain, intercepts, asymptotes and their behaviour, intervals of increase and decrease, and concavity, and to locate extrema and points of inflection. There is no need to graph the function. [10 marks] a) show that f(x)= [6 marks] 10. A cable television company is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides of a 100m wide river. The company has to connect points P and Q with cable, where Q is on the north bank 1200m east of P. It costs $40/m to lay cable underground and $80/m to lay cable underwater. What is the least expensive way to lay the cable? Hint: let the independent variable x represent the length of cable that will be laid underground? [10 marks]