Problem 12.2. The function f(x,y,a,b) is f (x,y,a,b) = a²x + xy² + y³ 1 + x² + y² + 1 + a? + by, 33 with (x,y,a,b) ER4. Find all of the local extreme points of the function: (a) Calculate the gradient of f(x,y,a,b). (b) Find all of the critical points [x,y,a,b) ER4 with degree f(x,y,a,b) = 0. %3D (c) Calculate the Hesse-matrix of f.

Q: A. Find the gradient of f. Vƒ = i+ j Note: Your answers should be expressions of x and y; e.g. "3x -…

A: Given that fx,y=xy.....(1), P=(2,1) and v→=-3 i^- j^. To find: (a) ∇f             (b) ∇f at P.…

Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: What is the gradient of the function f(x) = 2 e3x + 5 e7× 2 e3x 6 er +5 ex 5 e* F 2 ed + 35 e* 2+5…

A: The gradient function gives the slope of a function at any single point on its curve.

Q: g(x, y) = 2x² − 3y², (√8, √5) - Gradient is f(x, y) = tan Gradient is -1 ¹(). 9y (1,8)

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Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

Q: b Suppose we want to find all points at which the direction of fastest change of the function f(x,…

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Q: Prove that if two functions f(x, y) and g(x, y) have the same gradient, then they differ by at most…

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Q: (c) Vf(x, y, z) = (2xy, x² – 2yz, 4 - y²) -

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Q: 3. The line passing through (4, a) and (8, 1) has gradient 4. Work out the value of a. (CLO3)

A: Given two points (4,a) and (8,1) Gradient = 3/4

Q: First, compute the gradient of the function p(x,y) = √22-3x² - 4y². Then evaluate it at the point…

A: p(x,y)=22-3x2-4y2∇p(x,y)=<∂p∂x,∂p∂y>∂ ∂x(xn)=nxn-1

Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

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Q: Find the gradient of the function f(x,y) = 10y - 2x at the point (2,9). Then sketch the gradient and…

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Q: Question 2. Consider the function f(x, y) = x³-12xy + 8y³. (a) Find all the stationary points of the…

A: The saddle point is (0, 0)  Local minima is (2, 1)

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: For each of the following pairs of functions f and g, determine if the level curves of the functions…

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Q: (2,-4). At what point on the graph of f (x) = x² – 5x +2 is the gradient equal to 10? (12)

A: here this is the question of co-ordinate of function.  here we have to find slope of equation so the…

Q: (c) f(x1,x2, x3, X4) = 4x1 + 5x2 – X3 + x4 - (d) f(x1,x2, X3, X4) = -5 exp(x1)+ x2 · X4

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Q: Question 3 a. Find the gradient of r=x +y² + z?

A: The given problem is to find the gradient of given function r=√(x2+y2+z2) , we have to find the…