What are the absolute min and max of f(x,y)=xy^2 over a specific domain?

der.physika · 2010-02-27T10:51:28+00:00

Find the absolute min & absolute max of f(x,y)=xy^2 with domain x^2+y^2\leq4 Please help

Thread starter der.physika
Start date Feb 27, 2010
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In summary, an absolute max/min problem is a mathematical problem that involves finding the largest or smallest value of a function over a given interval or domain. It can be solved by taking the derivative of the function, setting it equal to zero, and solving for critical points. The difference between absolute max/min and local max/min is that the former refers to the largest or smallest value over a given interval, while the latter refers to the largest or smallest value within a specific region. The first derivative test is used to determine critical points in continuous and differentiable functions. Absolute max/min problems have real-life significance in various fields, such as economics, physics, and engineering, where they can be used to optimize functions and find the best possible outcomes.

Feb 27, 2010

der.physika

Find the absolute min & absolute max of

[tex]f(x,y)=xy^2[/tex]

with domain [tex]x^2+y^2\leq4[/tex]

Please help

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Feb 27, 2010

Dick

Science Advisor

Homework Helper

Look for critical points on the interior x^2+y^2<4 and then check the boundary x^2+y^2=4. You should be able to at least get started.

Related to What are the absolute min and max of f(x,y)=xy^2 over a specific domain?

What is an absolute max/min problem?

An absolute max/min problem is a mathematical problem that involves finding the largest (maximum) or smallest (minimum) value of a function over a given interval or domain.

How is an absolute max/min problem solved?

An absolute max/min problem can be solved by taking the derivative of the function, setting it equal to zero, and solving for the critical points. These critical points can then be plugged back into the original function to determine the absolute max/min values.

What is the difference between absolute max/min and local max/min?

The absolute max/min refers to the largest or smallest value of a function over a given interval or domain. Local max/min, on the other hand, refers to the largest or smallest value of a function within a specific region or neighborhood of a point.

When do we use the first derivative test for absolute max/min problems?

The first derivative test is used when the function is continuous and differentiable over the given interval or domain. It helps to determine the critical points where the function changes from increasing to decreasing or vice versa.

What is the significance of absolute max/min problems in real life?

Absolute max/min problems are commonly used in various fields such as economics, physics, and engineering, to optimize certain functions and find the best possible outcomes. For example, in economics, absolute max/min problems can be used to determine the maximum profit for a company or the minimum cost for a project.