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- Calculus 3
- Partial Derivative Applications
Lagrange multipliers
- Intro Lesson: a15:04
- Intro Lesson: b13:43
Lagrange multipliers
Lessons
Notes:
Lagrange Multipliers for 2 Variable Functions
Lagrange Multipliers for 3 Variable Functions
Lagrange Multipliers for 2 Variable Functions
Last section, we saw that it was a long process to calculate potential absolute max & mins on a boundary. Lagrange Multipliers help make this process easier and faster.
Suppose we have a function f(x,y), and we want to optimize this function when given a constraint function g(x,y). There are 2 steps we need to do:
- Solve the systems of equations:
fx=λgx
fy=λgy
g(x,y)=0 - Plug all the solutions (x,y) into the function f(x,y) to identify any maximums & minimum.
Lagrange Multipliers for 3 Variable Functions
Suppose we have a function f(x,y,z), and we want to optimize this function when given a constraint function g(x,y,z). Once again, there are two steps
- Solve the systems of equations:
fx=λgx
fy=λgy
fz=λgz
g(x,y,z)=0 - Plug all the solutions (x,y,z) into the function f(x,y,z) to identify any maximums & minimum.
- IntroductionLagrange Multipliers Overview:a)Lagrange Multipliers for 2 Variable Functions
- fx=λgx
- fy=λgy
- g(x,y)=0
- Identify any max & mins
- Example
b)Lagrange Multipliers for 3 Variable Functions- fx=λgx
- fy=λgy
- fz=λgz
- g(x,y)=0
- Identify any max & mins
- Example