Find the indicated maxima or minima.
-Minimum of $f(x, y, z)=x^{2}+y^{2}+z^{2}$, subject to $x+2 y-z=3$
A) $\frac{3}{2}$ when $x=\frac{1}{2}, y=1, z=-\frac{1}{2}$
B) 2 when $x=0, y=1, z=-1$
C) $\frac{9}{2}$ when $x=-\frac{1}{2}, y=2, z=\frac{1}{2}$
D) $\frac{54}{49}$ when $x=\frac{3}{7}, y=\frac{6}{7}, z=-\frac{3}{7}$

Question

Quizplus · Accepted Answer

Using Lagrange multipliers, we get $x=\frac{1}{2}, y=1, z=-\frac{1}{2}$ and the minimum value is $\frac{3}{2}$.

Find the Indicated Maxima or Minima f(x,y,z)=x2+y2+z2f(x, y, z)=x^{2}+y^{2}+z^{2}f(x,y,z)=x2+y2+z2 , Subject To

Find the Indicated Maxima or Minima $f(x, y, z)=x^{2}+y^{2}+z^{2}$ , Subject To