Your textbook should have a section on finding stationary points for functions of two variables. I'm reasonably certain it will also have a worked example or two.keighley said:Homework Statement
I have been asked to answer the following:
The function (x^3)+(y^3)-(2x^2)-(2y^2)+(3xy) has two stationary values. Determine their co-ordinates and their nature.
Homework Equations
The Attempt at a Solution
Sorry I am stuck.
Finding stationary values allows us to determine the relative maximum and minimum points of a function, as well as points where the function has a horizontal tangent.
To find the stationary values of a function, we set the derivative of the function equal to 0 and solve for the variable. The resulting value(s) will be the coordinates of the stationary point(s).
The nature of a stationary point tells us whether it is a maximum or minimum point, or a point of inflection, by analyzing the second derivative of the function at that point.
To determine the nature of a stationary point, we evaluate the second derivative of the function at that point. If the second derivative is positive, the point is a minimum. If the second derivative is negative, the point is a maximum. If the second derivative is 0, further analysis is needed to determine the nature of the point.
Finding stationary values can be useful in optimization problems, such as finding the maximum or minimum value of a cost or profit function. It is also used in physics and engineering to determine maximum and minimum points of velocity, acceleration, or other physical quantities.