# Lagrange Multiplier theory question

## Homework Statement

I made this up, so I am not even sure if there is a solution

Let's say I have to find values for which these two inequality hold $$x^2 + y^5 + z = 6$$ and $$8xy + z^9 \sin(x) + 2yx \leq 200$$

And by Lagrange Multipliers that

$$\nabla f = \mu \nabla g$$

So can I let $$f = 8xy + z^9 \sin(x) + 2yx - 200 \leq 0$$?

HallsofIvy
Homework Helper
What question are you trying to answer? Normally, the Lagrange multiplier method is used to find a maximum or minimum to a given function with some additional constraints. Here, you don't seem to have any function to maximize or minimize

What question are you trying to answer? Normally, the Lagrange multiplier method is used to find a maximum or minimum to a given function with some additional constraints. Here, you don't seem to have any function to maximize or minimize

Yeah I made one by making f <= 0...?

Okay I got this idea from another problem from this video

go to 5:05....

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Ray Vickson