Problem 9.2. Let f(x, y, z) = 5x + y - 3z. Determine whether f(x, y,z) has absolute extrema on the
intersection of the plane x + y + z = 0 and the sphere x2 + y² + z2 = 1. If the extrema exist, find them.

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?