Hw16-Lagrange-multipliers: Problem 7
Problem Value: 1 point(s). Problem Score: 89%. Attempts Remaining: 6 attempts.
Use Lagrange multipliers to find all the hot spots on the spherical surface $x^2 + y^2 + z^2 = 1$ where the temperature is given by $T(x, y, z) = xz + yz$.
(a) List all the points that are potential minimums or maximums
$(x, y, z) = (1/2, 1/2, 1/\sqrt{2}), (1/2, 1/2, -1/\sqrt{2}), (-1/2, -1/2, 1/\sqrt{2}), (-1/2, -1/2, -1/\sqrt{2}), (1/\sqrt{2}, -1/\sqrt{2}, 0), (-1/\sqrt{2}, 1/\sqrt{2}, 0), (0, 0, 1), (0, 0, -1)$
(Enter a comma separated list of points as needed)
(b) Final Answers
Maximum Value = $\sqrt{2}/2$
Minimum Value = $-\sqrt{2}/2$