# Optimization and Newton's method

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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

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https://brainmass.com/math/optimization/optimization-and-newton-s-method-55226

#### Solution Summary

This solution includes several optimization problem and an example of Newton's method.

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