F(x,y,z)=2x2+7y2+7z2 F(x,y,z)= 1152 The unit vector u for which the directional derivative is maximum at point (11,7,9) is ? What is the maximum directional derivative at the point (11,7,9) ?
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F(x,y,z)=2x2+7y2+7z2
F(x,y,z)= 1152
The unit
What is the maximum directional derivative at the point (11,7,9) ?
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- Find the velocity, speed, and acceleration of a particle moving with position function r(t)=(3t^2-4)i+(3t)j Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t=2You are standing above the point (2, 2) on the surface z = 15 - (3x² + 2y²). (a) In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction = (b) If you start to move in this direction, what is the slope of your path? slope =Directional derivative of p = 2xz - y2, at the point (1, 3, 2), becomes maximum in the direction of 1. 4i + 2j – 3k 4i — бј + 2k 3. 2i – 6j + 2k 4. 4i - бј - 2k 2.
- You are standing above the point (3, 3) on the surface z = 10 – (2x² + y²). (a) In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction = (b) If you start to move in this direction, what is the slope of your path? slope =Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 1, 1) in the direction of the vector √5 (Use symbolic notation and fractions where needed.) directional derivative: + 2 √5Find the maximum rate of change of f(x, y, z) = x + y/z at the point (4, -5, -4) and the direction (unit vector) in which it occurs. Maximum rate of change: (3(33)^.5)/16 Direction (unit vector) in which it occurs: (
- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = (2e-t, 2e^) (2, 2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) %3D s(t) : %D a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(0) %3D a(0) : (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the qiven point.Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point (4, - 5) The unit vector that is normal to the level curve of the function f(x, y) isVector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v = ()i + (_j.
- Find vector z + vector y if vector z= <1, 4> and vector y= <3, 0>. graphGive a vector parametric equation for the line through the point (4,-3) that is perpendicular to the line <1−4t,3t−3>Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction at the point P. (a) At the point P = (2, 2) in the direction = 7, the directional derivative is approximately (b) At the point P = (2, 3) in the direction = -3, the directional derivative is approximately (c) At the point P = (1,4) in the direction 7 = (i + j)/√√2, the directional derivative is approximately (d) At the point P = (1, 0) in the direction, the directional derivative is approximately 4.8 4 3.2 2.4 1.6 0.8 0 OH -0.8 2.0 -0.8 0.0 O 0 0.8 1.6 X 10.0 2.4 12.0 -2.0 3.2 16.0 18.0 14.0 8.0 4 (Click on graph to enlarge) 4.8