Can i have this as soon as possible please? I will give a rate!! or f(x, y, z) x2y + y2 + xz , compute a) the directional derivative at ( 1, 2, 4) in the direction of 12,2,1) , b) the maximum valu...
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks 6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x,y,z) = xy + y2 – 23 – 105. 1) vf = a. yi + (x + 2y); – 3z2K b. (y + y2)i + (x + 2y); - 3z2k c. xi + (y + 2y); - 3z2K d. None of the above a. b. C. d. 2) The direction in which ſ decreases most rapidly at A(0,1,1) is: a. 14 14 c. wait tasta d tai-haiti e. None of...
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 + z2 + 5 at the point (1, -3,2) in the direction of the vector < 1,0,-1>. (Hint: Use the results of partial derivatives from part(a))
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. 2) The direction in which f decreases most rapidly at A(0,1,1) is: 2 a. + 3 b. 是最+ i ++ d. 高+ C. 3 14 e. None of the above
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
Problem 4 a5 pts) La f(x,y,z) = 3x2+2+2 (a) Draw a few of the level surfaces (4.3.2) = c for admissible values of cand classify the type of surface these are (b) Compute the directional derivative of fat (1.2.3) in the direction of the vector û= 2.2.1). (c) Find the value and direction of the maximum rate of change off at the point(1.2.3).
Find the directional derivative of f at p in the direction of a. f(x,y,z)=xy+z^2; P(2,-2,2);A=i+j+k
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional derivative of f at the point (0,0,0) toward the point (1,2,0). b) Find the maximum rate of change of f at point (0,0,0). In which direction does the max rate of change at (0,0,0) does occur? (two questions here!)
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...