find the directional derivative of fxyz4xyz2fxyz4xyz2 at the point 224224 in the direction of a

So here f xy z is equal to 4 xy plus z squared and the point is 2 to minus 4 and angle pi by 3.

In this question we need to find, work done, and here the force field, F, we are given as x, com

Hello everyone, in this question we have to find direction derivative. So here we have our fx is

In this problem, we're given a three -dimensional function F that describes the concentration of

this question we have to find the directional derivative of the function f of x y z equals to x

Question

Find the directional derivative of f(x,y,z) = 4xy + z^2 at the point (2,2,-4) in the direction of a vector making an angle of π/3 with ∇f(2,2,-4). The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = 2x^2 + 2y^4 + 4x^2z^2 mg/cm^3. You are at the point (-1,-1,-1). (a) In which direction should you move if you want the concentration to increase the fastest? direction: (Give your answer as a vector.) (b) You start to move in the direction you found in part (a) at a speed of 33 cm/sec. How fast is the concentration changing? rate of change = Consider the function f(x,y) = -4x^2 - 2y^2. Find the directional derivative of f at the point (-3,-4) in the direction given by the angle θ = π/3. Find the unit vector which describes the direction in which f is increasing most rapidly at (-3,-4).

          Find the directional derivative of f(x,y,z) = 4xy + z^2 at the point (2,2,-4) in the direction of a vector making an angle of π/3 with ∇f(2,2,-4).

The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = 2x^2 + 2y^4 + 4x^2z^2 mg/cm^3. You are at the point (-1,-1,-1).
(a) In which direction should you move if you want the concentration to increase the fastest?
direction: 
(Give your answer as a vector.)
(b) You start to move in the direction you found in part (a) at a speed of 33 cm/sec. How fast is the concentration changing?
rate of change = 

Consider the function f(x,y) = -4x^2 - 2y^2.
Find the directional derivative of f at the point (-3,-4) in the direction given by the angle θ = π/3.
Find the unit vector which describes the direction in which f is increasing most rapidly at (-3,-4).

Added by Margaret B.

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