The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai
nts g(x,y,z)=0 and h(x,y,z)=0, where g and h are also differentiable, are gradientf=lambdagradientg+mugradienth, g(x,y,z)=0, and h(x,y,z)=0, where lambda and mu (the Lagrange multipliers) are real numbers. Use this result to find the maximum and minimum values of f(x,y,z)=xsquared+ysquared+zsquared on the intersection between the cone zsquared=4xsquared+4ysquared and the plane 2x+4z=2.
I think the correct answer from the choices listed above is option C. <span>The graph of a system of equations with the same slope and the same y-intercepts will never have no solutions. Rather, it has an infinite number of solutions since all points of the lines intersects.</span>