4 and 5

4. The wave heights h in the open sea is a function of the speed 1) of the wind and the length of time t that the wind has been blowing at that speed. The table below contains some values of the function h = f (v, t). Here his measured in feet, 1; in knots, and t in hours. Wave height (a) Est1mate(w1thun1ts) f1, and ft at the pomt (v,t) = (20,15). m 5 1o 15 20 so (b) What is the equation for the tangent plane to the graph of f at the 10 2 2 2 2 2 point corresponding to (v, t) = (20, 15)? 15 4 5 5 5 5 (c) Describe what f(25, 12) means, and use the tangent plane to ap- 20 5 7 B 8 9 proximate it. so 9 13 16 17 18 ((1) Estimate (with units) fw, fut, fw and ftt at the point (at) = 4 14 21 25 28 31 (20, 15). 5. To the right is a contour map for a function f that describes the topography of a park. (a) Estimate the values of f, fI and fy at the point (1', y) = (0.2, 0.3). (b) What is the equation for the tan- gent plane to the graph of f at the point corresponding to (ac, y) = (0.2,0.3)? >. (C) Estimate fzm, fzy, fyz and fit!!! at the point (1;, y) = (0.2, 0.3)