Problem 13 (6 points) Find the directional derivative of the function f(x,), 2) = 2 +...
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)?
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at 6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
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)...
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
please solve now (a) 3 marks The directional derivative of f(x,y) at a point P in the direction of the vector <2,3 > equals 7, and the directional derivative of f(x,y) at a point P in the direction of the vector < 1,-2 > equals 5. Find Vf at P. (b) 4 marks (c) 4 marks Find Zxy if z3 = xz+y. (d) 4 marks Find and classify all local extreme points of f(x,y) = x3 + y3 - 3x...
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz, (4,2, 8), v = (-1, -2, 2) Duf(4, 2, 8) = -4 X
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
Find the directional derivative of the function at the given point in the direction of vector v. f(x, y, z) - xel + ye? + zet, (0, 0, 0), v = <4,9,0> DULCO,0,0) - Need Help? Read it Talk to a Tutor
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