CalcIII extreme values and saddle points

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In summary, the conversation discusses how to solve a linear function with a raised power. The individual mentions separating partial derivatives and solving for (0,0) and another answer. They also mention using substitution to solve the function.
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chronie
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Homework Statement



http://img121.imageshack.us/img121/4601/54510849.png

The Attempt at a Solution



I separated the partial derivatives. However I do not know how to solve a linear function with a raised power. I know that I will have to solve for (0,0) and another answer. Yet, I just do not know how to solve for that power. Technically I can graph the functions but I cannot use a calculator in my clac class. If anyone can help me out that would be great.
 
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  • #2
I would solve the Fx equation for y and then substitute the y value into the Fy equation, and vice versa.
 
  • #3
oh I totally forgot about substitution. Thank you!
 

1. What is the difference between a maximum and a saddle point in Calculus III?

In Calculus III, a maximum point is where a function reaches its highest value, while a saddle point is a point on the graph where the function changes direction from increasing to decreasing or vice versa. Unlike a maximum point, a saddle point is not necessarily the highest point on the graph.

2. How do you find extreme values and saddle points of a multivariable function?

To find extreme values and saddle points of a multivariable function, you can use the second derivative test. First, find the critical points by setting the partial derivatives equal to zero. Then, calculate the second derivative at each critical point. If the second derivative is positive, the point is a minimum; if it is negative, the point is a maximum; and if it is zero, the test is inconclusive and further investigation is needed to determine if it is a saddle point.

3. Can a function have more than one saddle point?

Yes, a function can have multiple saddle points. This occurs when the function changes direction more than once on the graph.

4. What is the significance of saddle points in real-world applications?

In real-world applications, saddle points can represent points of equilibrium or stability. For example, in economics, a saddle point can represent the point at which supply and demand are equal, resulting in a stable market equilibrium.

5. Can a function have both a maximum and a saddle point?

Yes, a function can have both a maximum and a saddle point. This occurs when the function has a local maximum in one direction and a saddle point in another direction.

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