Purchase Solution

Find critical points and test for relative extrema.

Not what you're looking for?

Ask Custom Question

List the critical points for which the second partials test fails.


Purchase this Solution

Solution Summary

Critical points are found and a function is tested for extrema. The second partial test fails are listed for a function.

Solution Preview

First we find the critical points of the function f(x,y):
f1(x,y) is the first derivative with respect to x and f2(x,y) is the first derivative with respect to y. So:

f1(x,y) := 3*x^2-12*x+12
f2(x,y) := 3*y^2+18*y+27

We have to solve the system of f1=0 and f2=0 and find all the common (x,y) roots of both. As you can see f1 has no y element and f2 has no x component, so you can solve them separately.

f1=0 -> x=2, x=2 (repeated)
f2=0 -> y=-3, y=-3 (repeated)

Purchase this Solution

Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

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

Solving quadratic inequalities

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

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts