Question

Find a function f ( x , y ) such that ∇ f = ( x...

Find a function f ( x , y ) such that ∇ f = ( x 2 + y ) i + ( x + y ) j .

f ( x , y )=

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the directional derivative of the function at P in the direction of v. f(x, y)...
Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 − y3, P(8, 5), v = 2 2 (i + j)
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x,...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i by integrating P and Q with respect to the appropriate variables and combining answers. Then use that potential function to directly calculate the given line integral (via the Fundamental Theorem of Line Integrals): a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...
Find directional derivative of the function f(x, y, z) = 5x2 + 2xy – 3y2z at...
Find directional derivative of the function f(x, y, z) = 5x2 + 2xy – 3y2z at P(1, 0, 1) in the direction v = i + j – k .
. For the function f(x, y) = xye^x−y , at the point (2, 2) (a) find...
. For the function f(x, y) = xye^x−y , at the point (2, 2) (a) find the gradient. (b) find the directional derivative in the direction of the vector 3i − j. (c) in the direction of which unit vector is the rate of increase maximum? What is the maximum rate of increase? (d) in the direction of which unit vector(s) is the directional derivative zero?
the function f(x; y) = xye^x-y, at the point (2; 2) (1)find the gradient. (2) find...
the function f(x; y) = xye^x-y, at the point (2; 2) (1)find the gradient. (2) find the directional derivative in the direction of the vector 3i - j. (3)find the direction of which unit vector is the rate of increase maximum? What is the maxi- mum rate of increase? (4)find the direction of which unit vector(s) is the directional derivative zero?
For f(x,y)=ln(x^2−y+3). -> Find the domain and the range of the function z=f(x,y). -> Sketch the...
For f(x,y)=ln(x^2−y+3). -> Find the domain and the range of the function z=f(x,y). -> Sketch the domain, then separately sketch three distinct level curves. -> Find the linearization of f(x,y) at the point (x,y)=(4,18). -> Use this linearization to determine the approximate value of the function at the point (3.7,17.7).
Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the directional derivative of f 1+x^2+y^2 at...
Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the directional derivative of f 1+x^2+y^2 at the point (10, 6) in the direction of: (a) u = 3 i − 2 j (b) v = −i + 4 j
1. You are given the function f(x) = x/(1−x) a) Find the x and y- intercepts....
1. You are given the function f(x) = x/(1−x) a) Find the x and y- intercepts. b) Find the horizontal asymptote(s). c) Find the vertical asymptote(s) and do a limit analysis of the behavior of f on either side of each vertical asymptote. d) Find the critical number(s) of f. e) Find the interval(s) of increase and decrease of f. f) Find the relative maximum and minimum value(s) of f. g) Find the hypercritical number(s) of f. h) Find the...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the partial derivatives of the function f(x,y)=x^6y^6/x^2+y^2 fx(x,y)= fy(x,y)= part 3) Find all first- and second-order partial derivatives of the function f(x,y)=2x^2y^2−2x^2+5y fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 4) Find all first- and second-order partial derivatives of the function f(x,y)=9ye^(3x) fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 5) For the function given below, find the numbers (x,y) such that fx(x,y)=0 and fy(x,y)=0 f(x,y)=6x^2+23y^2+23xy+4x−2 Answer: x= and...
find the x and y intercepts of the function: f(x) = 2 | x + 2...
find the x and y intercepts of the function: f(x) = 2 | x + 2 | - 8