13. Find the directionsin which the directional derivative of f(x,y) = xe-ty at the point (2,0)...
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
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...
Problem 13 (6 points) Find the directional derivative of the function f(x,), 2) = 2 + y + y at the point (2,3,5) in the direction of the vector 21 - 3+2k. -0 1 2 3 Entered Answer Preview
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2. at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
Suppose f(x, y) = x2 + y2. Find the directional derivative of the function f at the point P(1, -1) in the direction of 7 = -31 + 4. That is, find Dif(1,-1). 5 14 O 14 5 O 14 5 O 5 14
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
(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))
3. Find the gradient ãf and the directional derivative at the point P(1,-1,2) in the direction a = (2,-1,1) for the function f(x, y, z) = xºz-yx + 2. In which direction is the directional derivative at P decreasing most rapidly and what is its value?
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).