Application of Differentiation : Exercise 4

Introduction
Exercise 4 will focus on Optimization problem.

1. Find two numbers whose sum is 243 and the product is a maximum.
2. Find two numbers if the product is 198 and the product is a maximum
3. Find the length and width of a rectangle that has the perimeter 125m and has a maximum area.
4. Find the point on the graph of the function closest to the given point g(x) = x³,(0, 5).
5. An open box is to be made from an 8.5 in by 11 in piece of paper by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume.