So I have to find the min and max values of f(x,y,z) = x^4 + y^4 + z^ 4 given the constraint x^2 + y^2 + z^2 = 1. I've found the points (+-1/sqrt(3),1/sqrt(3) ,1/sqrt(3)), (+-1/sqrt(3),-1/sqrt(3) ,1/sqrt(3)) ... etc all of which have the f-value of 1/3 when x =/= 0 & y =/= 0 & z =/= 0 (this will probably turn out to be the min?) My issue is the case when one value is zero and the other two are nonzero. I have 4x^3 = 2Lx (I'm using L for lambda here), then 2x^3 - Lx = 0, x(2x^2 - L) = 0....L = +-1/sqrt(2). From there, I have 2y^2 = L = 1/sqrt(2), y^2 = 1/2sqrt(2), and I'm not sure where to go from there for this case.