Purchase Solution

Four stationary points of a multivariable function

Not what you're looking for?

Ask Custom Question

A surface is described by the multivariable function f(x,y) where:

f(x,y) = x^3 + y^3 + 9(x^2 + y^2) + 12xy

a) Show that the four stationary points of this function are located at:

(x1, y1) = (0, 0)
(x2, y2) = (-10, -10)
(x3, y3) = (-4, 2)
(x4, y4) = (2, -4)

Purchase this Solution
Solution Summary

This shows how to find the four stationary points of a function.

Solution Preview

Stationary points are the points such that the partial derivatives of f(x,y) both with respect to x and y are 0.

Take the partial derivative of f(x,y) both respect to x and y to get

3x^2+18x+12y=0 (1)
3y^2+18y+12x=0 ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Critical Points of multivariable functions

    207306 Critical Points of Multivariable Functions Determine the critical points of the function: f(x1, x2) = (2 - x1 - x2)^2 + (1 + x1 + x2 - x1*x2)^2. Try to decide their nature. Please see the attached file for detailed solution.

  • Evaluating Stationary Points

    530205 Evaluating Stationary Points Using the function f(x)=2x^3+3x^2-36x+7 a) Find the stationary points of this function. b) i) Applying First Derivative Test, classify left hand stationary point in part a.

  • find out the stationary point, saddle point, min and max

    (a) Find all stationary points of the function amd enter their coordinates separated by ";", with at least 3 decimal places.

  • Stationary point

    545486 Stationary point This question concerns the function f(x)=x^3 +3x^2 −24x+40. (a) Find the stationary points of this function.

  • Function, derivatives, error, and stationary points.

    This provides a series of problems involving a function, including partial derivatives, second-order Taylor polynomial, least and greatest possible values, maximum possible error, rate of change, and stationary points.

  • Finding the Critical Points for Functions of Two Variables

    93777 Finding the Critical Points for Functions of Two Variables For the following function, find the critical points, determine their nature (maxima, minima, inflection, etc.) and clearly sketch the function showing all the coordinates: h(x, y) =

  • sketch the function and identify all stationary points

    Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down.

  • Absolute minimum and maximum

    These can only occur at critical points, namely: a) Stationary points where the partial derivatives are zero. b) Boundary points of the domain.

  • Time Series

    451494 Time Series Analysis Verify Question 1 Suppose that {Y_t} is stationary with autocovariance function ?_k. a) Show that W_t=?Y_t=Y_t-Y_(t-1) is stationary by finding the mean and autocovariance function for {W_t} . b) Show that U_t=?

View More Related Solutions