7) Find the derivative of the function at Po(-7,-8) in the direction of u = 121...
7) Find the derivative of the function at P.(-7.-8) in the direction of ū= 121 - 5j for f(x,y) = tan-
7) Find the derivative of the function at P. (-7,-8) in the direction of ū= 12i – 5j for f(x,y) = tan-1 -4633)
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks 6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
5. Find the directional derivative of the function at Pin the direction of u: a f( -2..2 f(x,y,z) = x2 + 2y2 - 3z-, P.(1,1,1), u = i +j+k.
Find the directions in which the function increases and decreases most rapidly at Po Then find the derivatives of the function in these directions f(x,y,z) = (x/y) - yz, Po(-3.1.4) The direction in which the given function f(x,y,z) = (x/Y)- yz increases most rapidly at Po(-3.1.4) isu = 11+( 1+ k (Type exact answers, using radicals as needed) The direction in which the given function f(x,y,z) = (x/y) - yz decreases most rapidly at Po(-3.1.4) is -u=1:-( k (Type exact...
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in those directions u f(x,y,z) = 4 In (xy) + 2 In (yz)+2 In (xz). Po(1,1,1) In which direction does the function increase most rapidly? (i+1+O (Type exact answers, using radicals as needed) In which direction does the function decrease most rapidly? = (1+) ;+ OK (Type exact answers, using radicals as needed.) What is the value of the...
Vectors: Using the direction -9i -5j and the point (6, -3), find the derivative of the function f(x) = -4xy-8y^2
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz, (4,2, 8), v = (-1, -2, 2) Duf(4, 2, 8) = -4 X
1) Find the directional derivative of the function at the given point and in the direction of the vector u as shown when f(x,y)= sen(2x+3y); (-6,4); u=(1/2)(sqrt(3)),-1) POSSIBLE ANSWERS A) sqrt(3)-(3/2) B) (3/2)+sqrt(3) C) (3/2)-sqrt(3) D) -(3/2)-sqrt(3) 2) Find the direction in which the function is growing or decreasing more rapidly at the point shown: f(x,y)=x(e^y)-lnx; (4,0) POSSIBLE ANSWERS: A) u=(3/(sqrt(265)) , 16/(sqrt(265))) B)u=(3/(sqrt(265)) , -16/(sqrt(265))) C)u=(16/(sqrt(265)) , 3/(sqrt(265))) D)u=(-3/(sqrt(265)) , 16/(sqrt(265)))
Find the directional derivative of the function at the given point in the direction of vector v. g(x, y, z) = (x + 2y + 5z)3/2, (8, 3, 7), v = 4j - k