Suppose f(x, y) = x2 + y2. Find the directional derivative of the function f at...
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
Answer the two parts. Label each your answers Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 3i - 4j Submit Answer Find the gradient of the function at the given point. Function Point f(x, y) = x + 9y V + 1 (8, 2) 11 1 Vf8, 2) = 1316 Find the maximum value of the directional derivative at the given point.
(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))
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!)
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
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)?
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
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...
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).
5. Find the directional derivative of the function at Pin the direction of u: a f( -2..2 f(x,y,z) = x2 + 2y2 - 3z-, P.(1,1,1), u = i +j+k.