Find the directional derivitive of f(x, y, z) xy at the point (4,1,1) that goes in...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Find the directional derivative of f(x,y,z)=xy+z^3 at the point (2,3,1) in the direction of a vector making an angle of 3π/4 with ∇f(2,3,1).
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
(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))
The directional derivative of a function f(x, y, z) = 2x²yz - 100 at the point Po(1,-1,-1) in the direction of a vector v = 2i + 2j + k is Select one: 2 A. 3 B. 2 C. D.O. E. None of these answers
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]
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
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) = xy + 23, P = (3, 7, 1). Calculate the directional derivative in the direction pointing to the origin. Remember to normalize the direction vector. Du f(3, 7, 1) =
Find the derivative of the function at P, in the direction of A. f(x,y,z) = xy + y2 + zx, (-2,2,1), A = 91 + 6j - 2k (PAD) (-2,2,1)= (Simplify your answer.)