Question

Describe the procedure for finding critical points of a function in two independent variables

Multivariable functions
ANSWERED
asked 2021-09-18
Describe the procedure for finding critical points of a function in two independent variables.

Expert Answers (1)

2021-09-19

Step 1
Based on the theorem on location of extrema, our aim is to
Determine \(\displaystyle{\frac{{\partial}}{{\partial{x}}}}{f{{\left({x},{y}\right)}}}\ \text{ and }\ {\frac{{\partial}}{{\partial{y}}}}{f{{\left({x},{y}\right)}}}\) if the exist, and then solve the system
Step 2
\(\begin{cases}\frac{\partial}{\partial x} f(x,y)=0\\ \frac{\partial}{\partial y} f(x,y)=0\end{cases}\)
The solution (if any) are the critical points to be further tested.

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