please answer 3 and 4 in detail thank you! (3). Find the first order partial derivatives...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
2. [3 marks] Consider the function f(x,y) = log (– 2y). (a) Find the partial derivatives (b) Find an equation of the tangent (plane) to the surface of f at the point (3,1, f (3,1)).
Find the first-order partial derivatives (fr. f,) and second-order partial derivatives (fxxıfyy, fxy, fyx) of the following functions. a. f(x,y)=x’y+x’y? +x+y? b. f(x, y) = (x + y)? Find the critical points at which the following function may be optimized and determine whether at these points the function is maximized, minimized or at a saddle point. z = 5x2 – 3y2 – 30x + 7y + 4xy
Partial derivatives Example Find the equation of the tangent plane and the normal line at the point (1,1,1) to the surface 2x2 + 2y2 + 3z2 = 6. Example Find the equation of the tangent plane and the normal line at the point (1, 2, 3) to the surface 2x2 + y2 – z2 = -3.
please help with 74,75,76. Thank you very much!! Find all first-order partial derivatives for the following multivariable functions. 74. f(x, y) = -4xy +5x+11 1(x,y) (x,y) 75. f(x, y)= -2erºsy LX. 4(x,y) 76. f(x, y)= /x' +2xy – 3y? 16x,y) L.(x2)
Differentiate implicitly to find the first partial derivatives of z. x In(y) + y2z + ? = 49 az Ox = az ay = 10. (-/1 Points] DETAILS ALC11 13.6.009. Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 5i - 123
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
Find all the first and second order partial derivatives for each of the following functions.(i.e. find fx, fy, fxx, fyy, fxy, and fyx). No need to simplify. (b) f(x, y) = x In V x2 + y2.
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
Q4: Fill in the blanks in the following: a. The first order partial derivatives Fulu, v) of the function (F(u, v)= u'sin(u+v+) equal b. The second order partial derivatives Fxx{x,y) of the function (F(x,y) =x’y-In (x²-y)) equal C. The tree diagram of the Chain Rule for the given function w=w(x,y),x=x( P.4.5), y=y(p,u,v), s=s(u,v)pap(t) will be ........... d. The result of Cross Product Dot Product is a... and the result of Dot Product a is a e. The projection of vector...