Let f(x,y) = (x – 2)² – (y – 2)². Fill in the blanks. f(2, 2) = 0 fa (2, 2) fy(2, 2) = 0 f(x, y) = (x – 2)² – (y – 2)² is at (2, 2). differentiable

Q: at the point

A:

Q: Jeremy and Thulile are running toward the point P along two straight paths that make a fixed angle…

A: Given: Jeremy and Thulile are running toward point P along two straight paths that make a fixed…

Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

A:

Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

A:

Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: The gradient of f(x, y) = xy at (x, y) = (2,3) is

A:

Q: Verify that the function ƒ(x) = x4 is concave up for x > 0and for x < 0. Is x = 0 an…

A:

Q: For f(x, y, z) = x^2 − 6x + y^2 + z^2 , describe and draw the level surface for the function value…

A: Let w=f(x,y,z) . The level surfaces of w=f(x,y,z) results, when w=k slices the the function,…

Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: Suppose f is differentiable with f(3) = 3 and f'(3) = -4. Suppose that g(z) = r* f(r). Find (3)-

A:

Q: find the critics (local max, lo cal min) Of the function f(xcy)= -x5+ Dy3+27x-24y+3

A:

Q: 3. Let z = yg(x2 - y²) be a differentiable function. Show that z(x,y) satisfies 1 дz 10z 7 - + - = х…

A:

Q: find the local extrema for the following function  f(x,y)= x^2 +y^2+xy-7x+4y+9

A:

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: Given F = (xyz², x²yz³, y²), find the following. (a). div (b). grad (divF) (c). curl (grad (divF))

A: We need to find the divergence of the field. F=xyz2, x2yz3, y2

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable…

A: Solution

Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: Examine the punction por vela tive extrema f6.y)= x-xy -y? -3x -y and so dde points %3D

A: Relative extrema and saddle point

Q: Does fx(x,y) when at (a,b), fy(x,y) has to be at (a,b) Explain why statement is true or explain why…

A: Let f(x, y) and its first and second derivatives are continuous at (a, b) and that, , then1) f has…

Q: 5 dy 6. If y is a differentiable function of x and x4 + 2y5 x³ = 5y2, then find dx

A:

Q: .. Find the absolute extrema of the function with its corresponding constrain. a) f(x, y) = x² - y²;…

A:

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: f(x.y) = x³y – . Calculate Se af and əx ду

A: