When we calculate the directional derivatives of the function f(x,y,z) = x3 +y* ++z° 4 at the point (1,1,1) in different directions, which of the following value(s) can we obtain? I:-8 П: -4 Ш:1 IV :5 V:6 (a) I, I, Ш, IV, V (b) I, Ш, IV, V (с) I, Ш, IV (d) II, III (e) Only III

Q: 3. Find the value of the directional derivative at the particular point Po for the given function in…

A:

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: Q2: a) If W =F(x,y), where x =v -g and y = 2vg calculate W +W, b) What is the directional derivative…

A: Given that w = Fx,y  , where x = v2 = g2 and y = 2vgWe have to calculate wx2 + wy2Now, we know that…

Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

A:

Q: 5. If the gradient of f(r, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing you the…

Q: If the gradient of f(x, y, z) at (1, 2, 3) is 2i – 2j +k, then the maximum value for a directional…

A:

Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

A:

Q: In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the %3D…

A: We have to find maximum directional derivative.

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

A:

Q: 1) Find the directional derivative of f at the given point P in the direction of the point. Q- f(r,…

A:

Q: The directional derivative of the function f (x, y, z) = x²z + xyz + y² in the direction of u = 2i +…

A:

Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v…

A:

Q: 1. Let f(x, y) = xcos(2x + y). a) Find the value of the directional derivative of f(x, y) at |in the…

A: Solve the following

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

A:

Q: The directional derivative of f(x, y) = In(x² + y²) at the point P(-5, 21) in the direction i = (9,…

A: Given  fx,y=lnx2+y2 To do find the directional derivative of fx,y at the point P-5,21 in the…

Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: Given- f(x,y)=20xx+y To find the directional vector of f(x, y) at P(5,0) in the direction of…

Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (1, -3) in the direction 0 The…

A: We have too find direction derivative.

Q: 1. Find the directional derivative of the function f(r, y, 2) = 3e" sin(ry) in the direction of v =…

A: 1.directional derivative formula = depf.n Del f = i∂f/∂x + j∂f/∂y+ k∂f/∂a given f = 3exsinxy…

Q: The directional derivative of f(1, y) at the point P = (0, 4) in the direction of the origin is -2.…

A: Given directional derivative of fx,y at point P =(0,4) in the direction of O(0,0) is -2. Here,…

Q: The directional derivative of the function f (x, y, z) = x²z + xyz + y? in the direction of u =…

A:

Q: The temperature of a solid is given by the function B(x, y,2) =x*y: +4x, where x, y, z are space…

A: Given temperature function Bx,y,z=xy+4x, given point P1,-2,1, and the direction a=2i-2j+k. Therefore…

Q: The directional derivative of f(x, y) = xe + 2y at point (2, 0) in the direction of the angle = is:…

A:

Q: Consider the function g(x, y) = 2e* sin y a) Prove that there are no critical points of g. b) What…

A:

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: The given scalar field is - f(x,y,z)=(x^2)z+(y^3)(z^2)-xyz

Q: 1. Let f(x, y) = x cos(2x + y). a) Find the value of the directional derivative of /(x, y) at| in…

A:

Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: B. Use the definition of directional derivative to solve Duf(x0, Yo, zo) at point P(xo, Yo%o) where…

A:

Q: 1. Let f(x, y) = x cos(2x+ y). a) Find the value of the directional derivative of f(x, y) at in the…

A:

Q: What is the directional derivative of the function f (x, y) = 2xy-3y² at point po- (5,5) in the…

A:

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

A:

Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

A:

Q: Find the directional derivative of the function at point P in the direction of v. f(x, y) = 3x + 4y…

A:

Q: Given a function (r, y, 2) = 3x2 + In (3y2+ 1) + e cos 2. i. Find the directional derivative of o at…

A: Here we will find out the required value.

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: NOTE:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: If f(x, y, 2) = cos(x - y)+e² , compute directional derivative of f at (5, 5, 0) in the direction of…

A:

Q: (2.2) The directional derivative of f (E, y) at P(1,2) in the direction of i+j is 2v2 and in the…

A:

Q: 6. Find the directional derivative of the function f (x, y, z) = x²z – xyz³ + xyz + y – 1 + z from…

A:

Q: Q2: a) If W = F(x ,y), where x =v²-g and y = 2vg calculate W +W, b) What is the directional…

A:

Q: 3 Find the directional derivatives of p = 8xyz³ - 2x²y²z² at the point (2,-1,1) in the direction 21…

A:

Q: Ctiofnal g(x, y) = V x² + y², _P(5, 12), v = 3i – 4j -

A: The partial derivatives of f at point (x,y)=(5,12) are :…

Q: Find the directional derivative of f(x, y, z) = 5y at P(5, 1, –4) x + z in the direction from P to…

A: We have to find directional derivatives for the given function.

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

A:

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.