The discussion focuses on finding local maximum and minimum values, as well as saddle points for the function f(x,y) = x² + xy + y² + y. The critical points are determined by calculating the partial derivatives, fx = 2x + y and fy = x + 2y + 1, and setting them equal to zero. The next step involves solving these equations to find the critical points (a,b) and testing them to classify the points as local maxima, minima, or saddle points.
PREREQUISITESStudents studying multivariable calculus, educators teaching optimization methods, and anyone interested in understanding critical points and their classifications in mathematical functions.
Physicsnoob90 said:Homework Statement
Find the local maximum and minimum values and saddle points of the function
f(x,y) = x^2 + xy + y^2 + y
Homework Equations
Local max/min
critical points
saddle
The Attempt at a Solution
1) partial derivative: fx = 2x+y fy = x+2y+1
from here, I'm a little confuse on what should i do to find the critical point in order to solve for the local max/min.