Solve the following maxima-minima problems using algebraic function. 1. Find two numbers having a sum of 9 if the product of one number by the square of the other is a maximum. Answer: 3 and 6 2. What is the smallest sum of two numbers if their product is 16? Answer: 4 and 4 3. A rectangular field of area 800ft2 is to be fenced off along a straight river. If no fencing is required along river, find the dimensions of the lot that will require the least amount of fencing. Answer: 40'x and 20' 4. Find the area of the largest rectangular garden that can be made so that one side of the house serves as the natural boundary and 10 m of fencing material is required for the remaining three sides. Answer: 5 m x =m