Please Answer Questions, Thank You!

Question 1 Fred makes an open metal container in the shape of a cuboid, as shown in the following diagram. X X y The container has height x m, width x m and length y m. The volume is 36m'. Let A (x) be the outside surface area of the container. (a) Show that A(x) =- +2x2. X (b) Find A'(x). (c) Given that the outside surface area is a minimum, find the height of the container. (d) Fred paints the outside of the container. A tin of paint covers a surface area of 10m and costs $20. Find the total cost of the tins needed to paint the container.Question 2 (Calculator is allowed) Let f(x) = -+2, for x> 1. x-1 (a) Write down the equation of the horizontal asymptote of the graph of f. (b) Find f'(x). Let g(x) = ae *+ b, for x 2 1. The graphs of f and g have the same horizontal asymptote. (c) Write down the value of b. (d) Given that g'(1) = -e , find the value of a. (e) There is a value of x, for 1