If f(x, y, z) = x² +y² – 4.xz, find the rate of change of f at P(3, 1, –2) in the direction from P to Q(-6, 3, 4). In what direction is f changing the fastest? What is the maximum rate of change of f?

Q: Allow f(x, y) = xe^(xy), now find the maximum rate of change of f at the point (3, -1).

A:

Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

A:

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

A:

Q: Let f(z, y) = re". What is the maximum rate of change of f at the point (2,0)? O a. V5 O b. 2 O c. 1…

A:

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, y)…

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: The temperature at any point (x, y) in a steel plate is T = 900 -0.7x² - 1.1y2, where x and y are…

A: topic- partial differentiation

Q: (a) Find the derivative of f(x, y, z) =x²- xy²- z at Po(5, 1, 0) in the direction of v=2i-3j+ 24k.…

A: Given: f(x, y, z) = x2 - xy2 - z, P0(5, 1, 0) and v=2i - 3j + 24k.

Q: e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given,

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: Is there a direction u in which the rate of change of ƒ(x, y) = x2 - 3xy + 4y2 at P(1, 2) equals 14?…

A:

Q: 5. Consider f(r, y) = x + 3y - (a) What is the domain of f(x,y)? (b) At P(2, –1) find the rate of…

A:

Q: 2) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

A:

Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Let f(x, y) = exy and P(1, 0). Solve for the gradient of f at the point P.

A:

Q: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

A:

Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

A:

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

A:

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

A:

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

A:

Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

A:

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Gradient problem....

Q: find the gradients of the functions below a)f (x, y, 2) = ye* + 22 in P(0, 2, :

A:

Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1…

A: Linear approximation to the function f(x ,y) at (a, b) :       L(x ,y) = f(a ,b) +(x-a) f x (a, b) +…

Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

A:

Q: The maximum rate of change of the function f (x, y, z) = x lIn(yz) at (1;2;-) is equal to: O 3 None…

A: We have to find the maximum rate of change of the function f(x,y,z)= x ln(yz) at (1,2,1/2).

Q: Let f(r, y) = re". What is the maximum rate of change of f at the point (2,0)? O a. 1 O b. V2 O .5 O…

A:

Q: The maximum rate of change of the function f (x, y, z) = x In(yz) at (1; 2; - is equal to: %3D O…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given function and the point are

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

A:

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: Consider the following function F (x, y, z) = x² + 2xyz + y² In z and the point P = (2,1, 1) and…

A: Consider the function, point and the direction  F(x,y,z)=x2+2xyz+y2lnzP=2,1,1u=i+2j−2k

Q: 4. Let f(x, y, z)= xy²z² - 2xyz a) Find the rate of change of f(x, y, z) at P(1, 1, -1) in the…

A: The gradient of a scalar function at any point describes the direction in which the scalar function…

Q: Find the maximum rate of change in f (x, y, z) = tan(r + 2y + 3z) at P = (-5,1,1).

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y)…

A:

Q: Let f(z, y) = ze. What is the maximum rate of change of fat the point (2,0)?

A:

Q: Find the values of constants a,b.c such that the maximum value of the directional derivative of f…

A:

Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

A:

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…