Show all work please! 1. Find the directional derivative of f(x, y) = x'y at (1,...
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
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...
Question 1. (15 pts) Given f(x, y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the directional derivative of f at P0 = (3, 2) in the direction of u = (5/13)i + (12/13)j. Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
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)?
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)...
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)
(5 points) (a): Find the directional derivative of \(f(x, y)=y^{2} \ln x\) at \(P(1,4)\) in the direction of \(\mathbf{u}=-3 \mathbf{i}+3 \mathbf{j}\)(b): Find the equation for the tangent plane and normal line to the surface \(\cos (\pi x)-x^{2} y+e^{x z}+y z=4\) at \(P(0,1,2)\)
Please answer all or do not answer. Thank you :) The Chain Rule and Directional Derivative: (a) Calculate by the chain rule given F(x,y) = x2 + y’, x = eu+20, y=uv. ov Use the chain rule (chain rule required!) to evaluate the partial derivative. OG where G(x,y) = x2 - y2 ,x=e"cosv, y = e"sinv. ди (c) Find the directional derivative in the direction of v=<12,-5> at (2,2) for f(x, y) = exy_y? and also the directional derivative in...
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
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).