Question

Lagrange Thorem Eplanation:

Let f and g have contious first partial derivatives such that f has an extremum at a point (x0,y0) on the smooth constraint curve g(x,y)=c

Answer 1

I am finda comfused about what this definition in my book, so f and g have first partial derivatives, f sub x and fsub y,, but then i get lost when its says" such that f has an stremum at the point (x0,y0) on the smooth constraint curve g(x,y)=c

Answer 2

can anybody exlain that a little better?

Answer 3

so is it saying that, that one of the partial derivaites from f, also creates of denotes an extremum(max or min) on the g(x,y)

Answer 4

?

Answer 5

yeah kinda confusing wording eh, i think it is talking about (lets say ) a Maximum point on g
where i have pushed the y-axis over into the corner,
g(x,y) {the wavy lines} is 'floating' above