S (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P ...
6. Let f(x,y) = xy+sin(x). Find all directions (unit vectors) so that the directional derivative off at the point (1,0) equals -
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. xy) =x"cos(y) +x"win(x) cos(x)sin(y). Plo The direction in which the given function txy_f(xy)-x3cos(v)+x2vsin(x) + cos(x)sin(y)increases most rapidly at P 0주 is u: " (Type exact answers, using radicals as n (xy)=x3cos(y)+x"win(x)-cos(x)sin(y) The direc on in which the given function f(xy- is eases most rapidly at (Type exact answers, using radicals as needed The derivative of the...
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 + z2 + 5 at the point (1, -3,2) in the direction of the vector < 1,0,-1>. (Hint: Use the results of partial derivatives from part(a))
Please help with this question. 10. Let S (x,y) = x2 + xy (a) Find the equation of the tangent plane at the point (1,0). (b) Use linear approximation at the point (1,0) to estimate f(1.1, -.1) (c) Find the derivative of fat (1,0) in the direction of the vector < 3,4 > (d) At the point (1,0), what direction is the function increasing most rapidly does not need to unit vector)? (e) How fast is it increasing in the...
please solve now (a) 3 marks The directional derivative of f(x,y) at a point P in the direction of the vector <2,3 > equals 7, and the directional derivative of f(x,y) at a point P in the direction of the vector < 1,-2 > equals 5. Find Vf at P. (b) 4 marks (c) 4 marks Find Zxy if z3 = xz+y. (d) 4 marks Find and classify all local extreme points of f(x,y) = x3 + y3 - 3x...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. 2) The direction in which f decreases most rapidly at A(0,1,1) is: 2 a. + 3 b. 是最+ i ++ d. 高+ C. 3 14 e. None of the above
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Find the directional derivative off at P in the direction of the vector U f(x,y,z) = x²lny P(5,1); U = wait à 1 = ( )
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
2. Let f(x,y) == xy + sin(x). Find a unit vector ū such that for the directional derivative Daf(7,0) one has Daf(1,0) = -_. 27+127. b. None of the other alternatives is correct. Ocū7-7