Let
a. Find at (2,1)
b. Find the directional derivative of f at (2,1) in the direction of -i+3j
Let a. Find at (2,1) b. Find the directional derivative of f at (2,1) in the...
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]
hi friends. I need the solution of all these questions Let us find the directional derivative of (a) f-: 3.rs_ Зуг in the direction j at (1.2.3). (b) f ะ: V.e2 +1,2 in the direction 2i + 2j + k at (0,-2,1). (c) ,f-sin(z) + cos(y) + sin(z) in the direction 2 +TJ at (r,0,T)
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at P(1,4) in the direction of u = -3i + 3j. (b): Find the equation for the tangent plane and normal line to the surface cos(70) – z’y+e*2 + y2 = 4 at P(0,1,2).
(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))
Question 5 Find the directional derivative off at P in the direction of a. f(x, y, z) = xy +z+; P(2, -2,2); a =i+j+k Duf = ? Edit
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)...
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
3 U + tyy = 0. 3. Find the directional derivative of f(x,y) 2In y at the point P(2,1) in the direction ū= 21+ 4. Find the linearization of f(x,y) = x2 + y2 at the point P(3, 4) and use it to
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