Homework Answers
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 +...
(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))
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the...
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the gradient of 1 Uf = 1 it -x/y^2 Note: Your answers should be expressions of x and y, eg "3x - 4y" j j B. Find the gradient off at the point P. (VA)(P) = 1 i+ -2 Note: Your answers should be numbers C. Find the directional derivative off at P in the direction of v. Duf = 9 Note: Your answer should...
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the...
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint g(x.). Enter the values of, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places y f(x,y) A-
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy +...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Find the derivative of the function at P, in the direction of A. f(x,y,z) = xy...
Find the derivative of the function at P, in the direction of A. f(x,y,z) = xy + y2 + zx, (-2,2,1), A = 91 + 6j - 2k (PAD) (-2,2,1)= (Simplify your answer.)
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g....
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
6. Let f(x,y) = xy+sin(x). Find all directions (unit vectors) so that the directional derivative off...
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 -
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off...
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off (b) (3 points) Find the directional derivative off at (1, 3, 0) in the direction of v= i +2j – k.
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
(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))
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the gradient of 1 Uf = 1 it -x/y^2 Note: Your answers should be expressions of x and y, eg "3x - 4y" j j B. Find the gradient off at the point P. (VA)(P) = 1 i+ -2 Note: Your answers should be numbers C. Find the directional derivative off at P in the direction of v. Duf = 9 Note: Your answer should...
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint g(x.). Enter the values of, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places y f(x,y) A-
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Find the derivative of the function at P, in the direction of A. f(x,y,z) = xy + y2 + zx, (-2,2,1), A = 91 + 6j - 2k (PAD) (-2,2,1)= (Simplify your answer.)
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
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 -
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off (b) (3 points) Find the directional derivative off at (1, 3, 0) in the direction of v= i +2j – k.
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
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