Suppose I have $a,b,c\ge-1$. If I wish to maximize the function $f(a,b,c)=a+b+c$ subject to the constraint $g(a,b,c)=a^5+b^5+c^5=0$, how do I proceed?
The usual way of partially differentiating $f(a,b,c)+\lambda g(a,b,c)$ and equating to zero gives me no critical points. What should do to find the critical points? How is the condition $a,b,c\ge-1$ to be used here? Any hints? Thanks beforehand.