Baumer8993 said:Homework Statement
Find the maximums, minimums, and saddle points (if any) of
Z = 4Y3 + X2 - 12Y2 - 36Y +2
Homework Equations
The partial derivatives with respect to X , and Y.
The Attempt at a Solution
I took the two partials, and set them equal to zero. The problem is that there is not anything to substitute, and when I tried solving them there was no solution.
The purpose of finding the minimums, maximums, and saddle points of a graph is to understand the behavior and characteristics of the graph. This information can be used to make predictions, optimize functions, and solve real-world problems.
To identify a minimum, maximum, or saddle point on a graph, you can use the first and second derivative tests. The first derivative test involves finding the critical points (where the derivative equals 0 or is undefined) and determining if they are local minimums, maximums, or saddle points. The second derivative test involves evaluating the second derivative at the critical points to determine if they are concave up (minimum) or concave down (maximum).
Yes, a graph can have multiple minimums, maximums, or saddle points. This can occur when the graph is complex or has multiple peaks and valleys.
A local minimum or maximum is the lowest or highest point within a small interval on the graph. It is only applicable to that specific region and may not be the overall lowest or highest point on the entire graph. A global minimum or maximum, on the other hand, is the lowest or highest point on the entire graph.
Finding the minimums, maximums, and saddle points can be applied in various fields such as engineering, economics, and physics. For example, in engineering, it can be used to optimize the design of a structure, in economics, it can help determine the most profitable price point for a product, and in physics, it can be used to predict the motion of an object.