9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
10. What is the average rate of change of 2 = f(x, y) = x+ + xy (with respect to horizontal distance) as one travels from (2,1) to (4,-2) ? 12 a) "The o the e) none of these 2 13 b) d) V13
Find the square of the maximum rate of change of f (, y) = xy + 2 (x) at the point (4,6), wherer (2) =42. The square of the maximum rate of change of the function is
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction 2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
8) a) About how much will f(x,y,z) = xy?z? change if the point (x,y,z) moves from (3.-7.-6) a distance of ds = 0.5 units in the direction of 21 +27 - K? b) Find the maximum change in f(x,y,z) in moving 0.5 units away in any direction, and indicated in what direction this occurs.
15. Find the instantaneous rate of change of f(x) = 4x - 2 at x = 5 16. Find the slone of the tangent lino to 2
Which one of the following is a linear transformation? O F(x, y) = xy O F(x,y) = (22,32) O F(x, y, z) = (x,y – 2,0) O F(x, y, z) = (2,4 – 2,1)
To find the instantaneous rate of change at x=3 Using the definition f(x +Ax) - f(x) Slope T - lim Ar-0 To find the instantaneous rate of change at x 3