Purchase Solution

Min, max and saddle points

Not what you're looking for?

Ask Custom Question

1) Find the local maximum and minimum values and saddle point(s). Here is the function:

f(x,y) = x^3y + 12x^2 -8y

2) Use Lagrange multiplier to find the extreme values (i.e. the max and min) of:

f(x,y) = 4x+6y

subjected to the constraint

x^2 + y^2 = 13

Purchase this Solution
Solution Summary

This solution shows the steps for determining the minimum value, maximum value, and saddle points for the given function. Additionally, this solution shows how to use the Lagrange multiplier to find the extreme values of a given function.

Solution Preview

1)

first we calculate the gradient and set them to zero

df/dx = 3(x^2)y + 24x = 0
df/dy = x^3 - 8 =0

this leads to one solution x = 2, y = -4.

Next, we use the second ...

Purchase this Solution
Free BrainMass Quizzes
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.

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.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

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

    The solution provides detailed explanation how to find out the stationary point, saddle point, min and max.

  • Finding critical points of a function z=f(x,y)

    If D > 0 and zxx > 0 the point is a relative min 2. If D > 0 and zxx < 0 the point is a relative max 3. If D < 0, Saddle point 4. If D = 0 need higher order tests.

  • Finding extreme values for functions of two variables

    Whether it would be called a saddle point is debatable. No, under most definitions.) Finally, to find whether the absolute max and min exist, we need to check what happens as x and y approach infinity. Along the line we see that .

  • Calculus

    Given f(x,y) = x^2-4xy+y^3+4y Find the critical points and then use the Saddle Point Derivative Test to determine if they are max, min, or saddle points. 2.

  • Critical points - sample question

    23171 Critical points sample question F(x,y)= xy + 8/x + 8/y Find the critical points of the given function and classify each as relative min., relative max., or a saddle point. See attachment.

  • Functions: Critical Points, Extrema and Saddle Points

    23170 Functions: Critical Points, Extrema and Saddle Points Find the critical points of the given function and classify each as relative minimum, relative maximum, or a saddle point.

  • The Hessian matrix and critical points

    26207 The Hessian Matrix and Critical Points Identify the critical points and determine their nature (local max, local min, saddle, degenerate) using the Hessian of the function f(x,y,z) = x^2+y^2+2z^2+xz. See the attached file.

  • Maximum, minimum, saddle points

    and minimum values and saddle points for a given function.

  • Max and Min Absolute Values

    The clue is wrong and your calculation for is wrong. . To find absolute max or min of in a closed interval, we should find the values of at the two end points and all the relative max and min values of .

View More Related Solutions