Given the function $f(x,y)=4x+2y$, I wish to find the extreme points (min,max) given the following constraint: $y=x^{2}+1, -3\leq x\leq 0$
The constraint contains both a condition and a region. Which way should I be using here ? Should it be lagrange multipliers, or should it be an extrema under a bounded region ?
In the second case, how do I find the min/max ? Can I say that the edges points over $y=x^{2}+1$ are (0,1) and (3,10) and there are no local points?
Thank you !
HINT: consider the function $$f(x,y)=f(x,x^2+1)=4x+2(x^2+1)$$ and you got a Problem in only one variable