Solve optimization problems: find maximum and minimum

optimize functions
solve equations
root finding faq
numerical methods
deadline tutorial
parametric equations

Optimization problem

Find the dimensions of the rectangle of largest area which can be inscribed in the closed region bounded by the x-axis, y-axis, and graph of f(x)=8-x3.

Graph for f(x)=8-x^3

If x is the width of the rectangle, we can conclude that 0<x<=2. Then the height of the rectangle is f(x). So the function that needs to be optimized is g(x)=x*f(x)=x(8-x3).

Graph for g(x)=x(8-x^3)

If you use DeadLine to find extrema, you will get x=1.25992105, which is the answer to the problem.

Solution of the problem

Another optimization problem:
A movie screen on a wall is 20 feet high and 10 feet above the floor. At what distance x from the front of the room should you position yourself so that the viewing angle of the movie screen is as large as possible ? See the solution.

Solve optimization problems, find maximum and minimum of a function using DeadLine.

DeadLine OnLine - free equation solver. Copyright 2003-2007 Ionut Alex. Chitu. | Contact | Sitemap