# How do you minimize and maximize #f(x,y)=x^3-y# constrained to #x-y=4#?

##### 1 Answer

we'll do it first as a problem in single variable calculus.

we have

it's all the usual stuff from here on

so

and

i'll do a **Lagrange Multiplier** next to compare. the basic premise is that with

plus the constraint

we can say that

or

So

**I'm asking for a second opinion on this next bit.**

Because there is no simple way to explore the nature of the turning points, especially with more complex problems, when using the LM approach. You can often play with the physical reality and reason a solution but there is no quick second derivative check, sadly, that i am aware of.

I am just wondering if the Hessian for let's say

would be of any use here.