[8 points) Find the directional derivative for g(x, y) = x’e-y at the point (3,0) in...
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
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
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
Answer the two parts. Label each your answers
Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 3i - 4j Submit Answer Find the gradient of the function at the given point. Function Point f(x, y) = x + 9y V + 1 (8, 2) 11 1 Vf8, 2) = 1316 Find the maximum value of the directional derivative at the given point.
1. Let f(x,y) = (2-7-% and g(x,y) = v f(x,y). J(1)(4 points) Find the maximum value of g(y). |(272 points) At which point(s) (x,y) and in the direction of which unit vector(s) ů does the maximum value for the directional derivative Dif(x,y) occur?
Stuck on this problemGiven the functionf(x,y)=ln(2x2+3y2)a) Find the directional derivative at (1,2) in the directionv=2i+3jb) Find the maximum rate of change and of f at the given pointand the direction at which it occurs.
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).
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
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(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...
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?