Problem 1. Let f(a:, y, z) : ln(.732 + 3/2 | 22). a) What is the direction of maximal increase of f at the point (1, l, 1)? b) At the point (1, 1, 1), llOW far in the direction found in (a) do you need to go to obtain an increase of 0.1 in f? c) At the point (1, 1, 1), how far in the direction of (1, 1, 2) do you need to go to obtain an increase of 0.2 in f? Problem 2. Consider the function f(:c, y) = my + i + 5 (a) What is its domain of denition? (b) Find the local minima, local maxima, and the saddle points for f. Problem 3. Consider the function f(;r, y) = m4 + 3/4. (a) Explain that (0,0) is a critical point. (b) What does the second derivative test say about the behaviour of f near (0, 0)? (c) In spite of the answer obtained for (b), explain that f has an absolute minimum at (0, 0)