4) Find a positive number such that the sum of the number and its reciprocal is as small as possible
6) Find the dimensions of a rectangle with area 1000m^2 whose perimeter is as small as possible
10) A box with square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize the amount of material used.
16) Find the point on the line 6x+ y = 9 that is closest to the point (-3,1).
Use Newton's method to find all roots of the equation correct to six decimals
√x + √3 = x^2
This solution includes several optimization problem and an example of Newton's method.