Good point - I failed to check that claim.Karnage1993 said:How is the determinant 0?
A simple multivariable extrema is a point where the value of a multivariable function is either at its highest or lowest point.
To find the extrema of a simple multivariable function, you must first take partial derivatives with respect to each variable and set them equal to zero. Then, solve the resulting system of equations to find the critical points. Finally, use the second derivative test or a graphical method to determine the nature of the critical point and whether it is a maximum or minimum.
The second derivative test involves taking the second derivative of a function at a critical point. If the second derivative is positive, the critical point is a minimum. If the second derivative is negative, the critical point is a maximum. If the second derivative is equal to zero, the test is inconclusive and further analysis is needed.
Yes, a simple multivariable function can have multiple extrema. This can occur when there are multiple critical points or when the function has a saddle point, where it is neither a maximum nor a minimum.
The concept of extrema is applied in various fields of science, such as economics, physics, and engineering. For example, in economics, extrema can be used to determine the maximum profit or minimum cost for a business. In physics, extrema can be used to find the maximum or minimum speed of an object in motion. In engineering, extrema can be used to optimize the design of a structure or system.